Term
For a quadratic function (i.e. f(x)=3x^24x+7), to determine the vertex by calculator you must _________________. 

Definition
use the 'maximum' function (when the parabola is opening down) or the 'minimum' function (when the parabola is opening up)  both of these are found in the 'calc' menu 


Term
T/F: A situation involving 'direct variation' is one in which the 2 variables, x and y, both increase and decrease together. 

Definition
True (i.e. as speed increases, number of speeding tickets increases) 


Term
T/F: A situation involving 'inverse variation' is one in which the 2 variables, x and y, both increase and decrease together. 

Definition
False, inverse variation is when x increases, y decreases and visa versa (i.e. The more time and money I spend working on my car, the less time I will spend stranded somewhere) 


Term
The restrictions on the equation are 3/x=8/(x+3) are ____. 

Definition


Term
The main concept of Inverse Functions is that when comparing a function and its inverse, all x and y information is _______. 

Definition


Term
If you're given a sequence of numbers (i.e. 1,1,2,3,5,8,...) and asked to form an inputoutput table, the inputs will be ______. 

Definition
the natural numbers (1,2,3,4,5,6,...) 


Term

Definition


Term

Definition


Term
The 'initial value' of a function is the function's _______. 

Definition


Term
When solving an equation for x, you can ALWAYS __________. 

Definition
set the left side of the equation to y1, set the right side of the equation to y2, and see where they intersect! 


Term
The units for the slope of a function are always the ______ divided by the ______. 

Definition
units for y; units for x (i.e., if x is time measured in hours and y is distance measured in miles, then the units of slope will me 'miles/hour'.) 


Term
To find the slope of a line that passes through 2 given points, we would use the formula ________. 

Definition


Term
To write P in terms of Q means to solve for ____. 

Definition


Term
If a quadratic function opened down (vertex is a maximum point) and the vertex is (3,4), then the range would be_______. 

Definition
y less than or equal to 4. 


Term
Solution to a system of equations 

Definition
The pair of x and ycoordinates that satisfy both equations 


Term
The Substitution Method will always/never/sometimes work for solving a system of equations. 

Definition


Term
The Graphing Method will always/never/sometimes work for solving a system of equations. 

Definition


Term
When factoring trinomials, the first method to try is ______. After doing that, the next method to try is the ________. 

Definition


Term
On you calculator, when a number has the E (i.e. 8.9456234E6), your calculator is providing an answer in _________ notation. 

Definition


Term
For a parabola, the range always begins at the ______. 

Definition
ycoordinate of the vertex 


Term

Definition
A flat, twodimensional surface extending forever in all dimensions (kind of like a superhuge piece of paper that goes on forever) 


Term
On the TI calculator, to access the table press _______. 

Definition


Term
If the yintercept of a line is 4 and the slope of the line is 6, the equation of the line is _____. 

Definition


Term
For the equation y=4x+10, the slope can be written as a fraction. In that case it would be _____. 

Definition


Term
T/F: Similar triangles have angles that are the same size. 

Definition


Term

Definition
The middle number in a set of ordered numbers 


Term

Definition
Things that are multiplied together (i.e. In the term 4yz, 4, y, and z are the three factors of the term) 


Term
T/F: Division by 0 is okay. 

Definition


Term
When subtracting 2 numbers that have the same sign, the answer will be positive always/never/sometimes. 

Definition
Sometimes (i.e. 32=+1 but 3(2)=1 


Term
T/F: The following terms are NOT like terms. 3xyz, 2.5yzx 

Definition
False, they have the same variables 


Term

Definition


Term

Definition
The sum of all sides (i.e. the distance around an object or shape) 


Term

Definition
How much space there is on a surface (i.e. how much space on a wall or on a table) 


Term

Definition
The average of a set of numbers. 


Term

Definition
Add up all numbers in the problem and divide by how many you added together 


Term

Definition
Put the numbers in order and if there's an odd number of numbers, the middle number is the median. Otherwise, take the two numbers that are in the middle and find their mean. 


Term

Definition
Terms that have the EXACT same collection of variables 


Term

Definition
Least Common Denominator (the LCM of the denominators) 


Term

Definition


Term

Definition
The number that is multiplied by a variable (i.e. 3 is the coefficient of 3x) 


Term

Definition
The result of flipping a fraction (i.e. the reciprocal of 2/3 is 3/2) 


Term

Definition
A collections of numbers and/or variables that are multiplied together (i.e. 3x + 4yz, 3x and 4yz are separate terms) 


Term

Definition
A single term (i.e., 3x, 4y, 8qw) 


Term

Definition
Two terms (i.e. 4x+7y, 9h+6R) 


Term

Definition
Three terms (i.e. 3D5J+4, 2x+3y+6L) 


Term
T/F: 0 divided by anything is 0. 

Definition


Term
When dividing by a fraction you must ________. 

Definition
First flip the second fraction (get its reciprocal) and then change the division to multiplication. 


Term

Definition
PEMDAS Parentheses Exponents Multiplications & Divisions Additions & Subtractions 


Term
In simplifying an expression, you always do it from ______ to ______. 

Definition


Term

Definition
Something WITHOUT an equal sign 


Term

Definition
Something WITH an equal sign 


Term
When multiplying 2 numbers that have the same sign (both positive OR both negative) the answer will be _______. 

Definition


Term
When multiplying 2 numbers that have different signs (one positive and one negative) the answer will be _______. 

Definition


Term
When dividing 2 numbers that have the same sign (both positive OR both negative) the answer will be _______. 

Definition


Term
When dividing 2 numbers that have different signs (one positive and one negative) the answer will be _______. 

Definition


Term
When adding 2 numbers that have the same sign, the answer will be positive always/never/sometimes. 

Definition
Sometimes (i.e.3+6=+9 but 3+(6)=9) 


Term

Definition


Term

Definition


Term
T/F: The square root of 16 has no real number solution 

Definition
True, negative numbers do not have real number square roots 


Term
How many terms are in the expression? 2x+3y4xyz 

Definition
3, Remember that addition and subtraction separate terms. 


Term

Definition


Term

Definition


Term
Before you cancel a factor out of the top and the bottom of an algebraic expression, you must first be able to _________. 

Definition
FACTOR out of the top and the bottom whatever it is you wish to cancel. 


Term
When dividing by a fraction you must _________ the ________ fraction. 

Definition
Flip (get the reciprocal), Second 


Term
The only time you can cancel a factor between a pair of fractions is when the two fractions are being ___________. 

Definition


Term
DEGREE OF A TERM (Monomial) 

Definition
The sum of the exponents on the variables (i.e. 4xyz has degree 3, 15xQ^5 has degree 6) 


Term

Definition
Find the degree of each term and whichever one is the biggest is the degree of the entire polynomial. 


Term
When you add or subtract, you must have _________. 

Definition


Term
When you add or subtract fractions, you must have ___________. 

Definition
Common denominators AND like terms 


Term
T/F: The sign in front of a number (just to the left of it) stays with that number. 

Definition


Term

Definition
A number that can only be divided by 1 and itself. 


Term

Definition
A number that can be divided by at least 1 other integer besides 1 and itself 


Term

Definition
A number in the following set: ...,3,2,1,0,1,2,3,... 


Term

Definition


Term

Definition
The largest integer that divides into both numbers (i.e. The GCF of 16 and 24 is 8) 


Term

Definition
The smallest integer that both numbers divide into (i.e. The LCM of 6 and 16 is 32) 


Term

Definition
How much room there is inside of something (i.e. inside a box or a freezer) 


Term
When plugging a number into an expression, it's a good idea to put ________ around the number. 

Definition


Term

Definition
An expression whose highest power of x is 1 


Term
"Twenty less than a number" translates into___________. 

Definition
x20 (NOTE: The answer is NOT 20x) 


Term

Definition
Angles that add up to 90 degrees 


Term

Definition
Angles that add up to 180 degrees 


Term
The angles of a triangle always add up to _______. 

Definition


Term
When doing operations on mixed numbers it is a good idea to first _________. 

Definition
Convert all mixed numbers to improper fractions 


Term
T/F: When evaluating the square root of a fraction you MUST first rewrite the problem as the square root of the numerator divided by the square root of the denominator. 

Definition
False, you can do that but you don't have to 


Term
To find the horizontal asymptote of a function, you must first compare the ______ of the numerator with the ______ of the denominator. 

Definition


Term
To find the vertical asymptotes of a function, you must ____________. 

Definition
Set the denominator to zero and solve. 


Term

Definition
Where the xaxis and yaxis intersect 


Term
The coordinates of the origin are _____. 

Definition


Term

Definition
A rule wherein xvalues are NOT repeated (used more than once) 


Term

Definition
All the numbers that when plugged into a function for x, yield an answer 


Term

Definition
All the yvalues that a function uses 


Term

Definition
Where the graph of a function intersects (touches) the xaxis. 


Term
To find the xintercept of a function you must _________. 

Definition


Term

Definition
Where the graph of a function intersects (touches) the yaxis. 


Term
To find the yintercept of a function you must _________. 

Definition


Term
Why do I set x=0 to find the yintercept of a function? 

Definition
Because yintercepts are on the yaxis and every point on the yaxis has an xcoordinate = 0 


Term
Why do I set y=0 to find the xintercepts of a function? 

Definition
Because xintercepts are on the xaxis and every point on the xaxis has a ycoordinate = 0 


Term

Definition
Angle that is less than 90 degrees 


Term

Definition
Angle that is more than 90 degrees 


Term

Definition
A 90 degree angle (i.e. like the angle formed where the wall and the floor meet) 


Term

Definition


Term

Definition
A straight, onedimensional figure extending forever in BOTH directions 


Term

Definition
A straight, onedimensional figure extending forever in one direction from a single point; in other words, half a line 


Term

Definition


Term

Definition
Angles that have the same measure (are equal) 


Term

Definition
Lines that meet at a right angle (like the crossbeams of a standard kite) 


Term

Definition
A triangle with ONE right angle 


Term

Definition
A triangle with THREE acute angles 


Term

Definition
A triangle with ONE obtuse angle 


Term

Definition
A triangle with all sides equal and all angles equal (in this case the angles will all be 60 degrees) 


Term
On the coordinate plane, the first quadrant is found in the ________corner. 

Definition


Term
On the coordinate plane, the second quadrant is found in the ________corner. 

Definition


Term
On the coordinate plane, the third quadrant is found in the ________corner. 

Definition


Term
On the coordinate plane, the fourth quadrant is found in the ________corner. 

Definition


Term
When converting a fraction to a decimal, divide the _______ by the ________. 

Definition


Term
To compare fractions to see which one is bigger you can either _______ or _______. 

Definition
Get common denominators, Convert both fractions to decimals 


Term
To change a percent to a decimal, you must move the decimal point ______. 

Definition


Term
To change a decimal to a percent, you must move the decimal point ______. 

Definition


Term
To enter a function into the calculator you must press the button labeled _____. 

Definition


Term
(3,0) is a ___intercept. 

Definition


Term
(7,0) is a ___intercept 

Definition


Term

Definition


Term
(0,8) is a ___intercept 

Definition


Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form. 

Definition


Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form. 

Definition


Term
In a linear equation, when Y is by itself, the slope is ALWAYS the number _________ by x. 

Definition


Term
In a linear equation, when Y is by itself, the Yintercept is ALWAYS the number _________ to x. 

Definition


Term
A handy way to remember slope is _______ over _______. 

Definition


Term
When we say "slope is rise over run" the 'rise' means the difference in the __________ from one point to another. 

Definition


Term
When we say "slope is rise over run" the 'run' means the difference in the __________ from one point to another. 

Definition


Term
T/F: In the expression 79, the two negatives can both be changed to positives. 

Definition
False, in order to be able to change them both to positives, they have to be right next to each other. 


Term
T/F: In the expression (9), the two negatives can both be changed to positives. 

Definition


Term
T/F: If a fraction is negative, it doesn't matter if the negative is applied to the NUMERATOR or the DENOMINATOR or in front of the fraction. 

Definition


Term

Definition
What you plug into a function for x 


Term

Definition
The result after you plug in a number for x into a function 


Term

Definition
The horizontal axis of a graph 


Term

Definition
The vertical axis of a graph 


Term
T/F: Addition is commutative 

Definition


Term
T/F: Subtraction is commutative 

Definition
False (i.e. 23 does not equal 32) 


Term
T/F: Multiplication is commutative 

Definition


Term
T/F: Division is commutative 

Definition
False (i.e. 2/3 does not equal 3/2) 


Term
If a variable does not appear to be multiplied by a number, then its coefficient is ____. 

Definition


Term
When multiplying 2 things together, you may add their exponents only when _________. 

Definition
The bases of the exponents are the same (i.e. x^2*x^3=x^5) 


Term
The only time you ever multiply 2 exponents by each other is when ______. 

Definition
One exponent is raised to the power of another (i.e. (x^2)^3=x^6) 


Term
Cubic inches are used for measuring ________. 

Definition


Term
Cubic feet are used for measuring ________. 

Definition


Term
Cubic meters are used for measuring ________. 

Definition


Term
Square inches are used for measuring ________. 

Definition


Term
Square feet are used for measuring ________. 

Definition


Term
Square meters are used for measuring ________. 

Definition


Term

Definition


Term
Another way to write 4<=x<9 is____. 

Definition


Term
Another way to write x>8 is ______. 

Definition


Term
If the equation for renting a jackhammer is y=35x+50, the 50 probably means ________. 

Definition
The initial rental fee (up front). 


Term
If the equation for renting a jackhammer is y=35x+50, the 35 probably means ________. 

Definition


Term
If an equation begins as: 3x11=7 and changes to become: 3x=18, what happened? 

Definition
Eleven was added to both sides 


Term
After solving an equation for the given variable, a way to check your work is to ____________. 

Definition
Plug your solution into the ORIGINAL problem for the variable and make sure both sides of the equation are equal. 


Term
If you have a function f(x)=3x7, then f(5) means _______. 

Definition
The yvalue that is paired up with the xvalue, 5. 


Term
If you have a function g(x)=86x, then g(3) means _______. 

Definition
The yvalue that is paired up with the xvalue, 3. 


Term
On the TI calculator, to access the graph press _______. 

Definition


Term
On the TI calculator, to access the table setup screen, press _______. 

Definition


Term
On the Table Setup screen on the TI calculator, the first number tells you _______. 

Definition
What will be the first xvalue displayed on your Table 


Term
On the Table Setup screen on the TI calculator, the second number tells you _______. 

Definition
What your xvalues will increase by on the Table 


Term
The best way to solve 3x8=4 is to first move the ____ to the other side of the equation then move the _____. 

Definition


Term
When you see the phrase "in terms of", the variable that comes directly before the phrase is the ________ variable. 

Definition


Term
When you see the phrase "in terms of", the variable that comes directly after the phrase is the ________ variable. 

Definition


Term
To solve the equation: PV=nRT for the variable R, you would need to ________ both sides of the equation by _____. 

Definition


Term
To solve the equation: A=3r^2 for the variable r, you would need to ________ both sides of the equation by _____ and then ______ of both sides. 

Definition
Divide, 3, take the square root 


Term
If a relation passes the Vertical Line Test, ________. 

Definition


Term
If a relation doesn't pass the Vertical Line Test, ________. 

Definition


Term
If a relation uses a value for x more than once, ________. 

Definition


Term
If a relation uses a value for y more than once, it ____ a function. 

Definition
May or may not be a function (how often the yvalues get uses has no bearing on whether or not it is a functiononly if you use an xvalue more than once) 


Term
T/F: The relation (1,6),(2,6),(3,6),(4,6) is a function. 

Definition


Term
T/F: The relation (6,1),(6,2),(6,3),(6,4) is a function. 

Definition


Term
Like a book, graphs are read from _____ to _____. 

Definition


Term
If the graph of a line goes down, from left to right, it has a ____ slope. 

Definition


Term
If the graph of a line goes up, from left to right, it has a ____ slope. 

Definition


Term
If the graph of a line is flat (horizontal), from left to right, it has a ____ slope. 

Definition


Term
Xintercepts of functions are found by setting ____ equal to _____ and then solving. 

Definition


Term
Yintercepts of functions are found by setting ____ equal to _____ and then solving. 

Definition


Term
When the equation of a line is in slopeintercept form, the number multiplied by X is the ____. 

Definition


Term
When the equation of a line is in slopeintercept form, the number added to X is the ____. 

Definition


Term
Slope is represented by the variable ____. 

Definition


Term
Yintercepts are represented by the variable ___. 

Definition


Term
When the equation of a line is in slopeintercept form, _______. 

Definition


Term
The slope of the equation y=3x9 is ____. 

Definition


Term
The yintercept of the equation y=3x9 is ____. 

Definition


Term
The slope of the equation y=39x is ____. 

Definition


Term
The yintercept of the equation y=39x is ____. 

Definition


Term
Two lines are parallel if their slopes are _____ AND if their yintercepts are _____. 

Definition


Term
Two lines are perpendicular if their slopes _____. 

Definition


Term
A 'proportion' is ________. 

Definition
A single fraction equal to a single fraction (i.e. 3/x = 2/5) 


Term
There are _____ centimeters in a meter. 

Definition


Term
There are _____ meters in a kilometer. 

Definition


Term
There are _____ millimeters in a centimeter. 

Definition


Term
There are about _____ centimeters in an inch. 

Definition


Term
T/F: Similar triangles have sides that are the same lengths. 

Definition
False, (rather they are proportional to each other) 


Term
Solution to a system of equations 

Definition
The point(s) at which the graphs of the 2 equations intersect 


Term
Solution to a system of equations 

Definition
The x and ycoordinates that satisfy both equations 


Term

Definition
Equations that have the SAME slope and DIFFERENT yintercepts 


Term

Definition
Equations that are the same (more easily viewed when you solve for y in both equations) 


Term
Coincident Equations have ______ solutions. 

Definition


Term
In solving a word problem, always set the variable equal to __________. 

Definition
whatever you're asked to solve for 


Term
The first step of the Substitution Method for solving a system of equations is to __________. 

Definition
isolate either of the variables in either equation 


Term
Choose One of the Three Choices. The Elimination Method will always/never/sometimes work for solving a system of equations. 

Definition


Term
Choose One of the Three Choices. The Graphing Method will always/never/sometimes work for solving a system of equations. 

Definition


Term
When solving a system of equations using the Elimination Method, you must always first make certain that both equations ____________. 

Definition
have all terms lined up (i.e. xterms above xterms, yterms above yterms, etc.) 


Term
When graphing linear inequalities, use a dotted line when there is ___________. 

Definition
a "less than" or "greater than" sign 


Term
When graphing linear inequalities, use a solid line when there is ___________. 

Definition
a "less than or equal to" or "greater than or equal to" sign 


Term
When a linear inequality is of the form y 

Definition


Term
When a linear inequality is of the form y>mx+b, shade ________ the line. 

Definition


Term
When factoring polynomials, the first factoring technique to try is always ______. 

Definition


Term
When factoring polynomials, the first method to try is ______. After doing that, the next method to try is the ________. 

Definition


Term
When factoring a quadratic binomial, it can sometimes be helpful to try using the _________method. 

Definition


Term

Definition
Numbers and variables that are MULTIPLIED together 


Term

Definition
Numbers and variables that are ADDED together 


Term
True or False: When factoring a binomial using the Difference of Squares method, you MUST write the '' term first and the '+' term second. (i.e.x^29=(x3)(x+3) but x^29does not=(x+3)(x3) 

Definition


Term
True or False: As a student, it would be a SUPREMELY good idea to learn how to factor polynomials right away and not "wing it" through MATH 65 and on into MATH 70. 

Definition


Term
When factoring the polynomial: 3x^2+12x+9 the first factoring technique to be attempted should be ______. The second method to be attempted is _________. 

Definition


Term
When you have an expression in which there is a 'power to a power' (i.e. (3^2)^5) you should ________ the powers. 

Definition


Term
When you have an expression in which you are multiplying two powers and the bases of the exponents are the same (i.e. 4^5*4^8), you should _________ the exponents. 

Definition


Term
When you have an expression in which you are dividing two powers and the bases of the exponents are the same (i.e. 4^5/4^8), you should _________ the exponents. 

Definition


Term
Anything (except 0) raised to the power of 0 is equal to ____. 

Definition


Term
True or False: Negative exponents make the whole problem negative. 

Definition
False, a negative sign in an exponent has NOTHING TO DO WITH THE SIGN OF THE ANSWER. 


Term
When switching from a positive exponent to a negative exponent (or visa versa), this will cause the expression to _______. 

Definition
be flipped (i.e. (2/3)^4 = (3/2)^4 


Term
On you calculator, when a numbers with the E (i.e. 8.9456234E6), your calculator is providing an answer in _________ notation. 

Definition


Term
In a right triangle, the _______ is always the longest side. 

Definition


Term
In a right triangle, the 2 sides that form the right angle are called the _____ of the right triangle. 

Definition


Term
True or False: In a right triangle, the hypotenuse is one of the sides that helps form the right angle. 

Definition
False, the hypotenuse NEVER helps form the right angle 


Term
The square root of a number(or variable) is the same as that number raised to the ____ power. 

Definition


Term
When you square the squareroot of a number, your answer is always ________. 

Definition


Term
A radicand is what is ________ a radical sign. 

Definition


Term
In the Real Numbers, a radicand must always be: (a) greater than zero (b) greater than or equal to zero (c) less than zero 

Definition


Term
When solving a radical equation, begin by doing what to both sides of the equation. 

Definition


Term
To determine the xintercepts of a function, we replace y with 0 and then solve. The reason is because ________. 

Definition
xintercepts are always on the xaxis and therefore always have a ycoordinate of 0 


Term
To determine the yintercept of a function, we replace x with 0 and then solve. The reason is because ________. 

Definition
yintercepts are always on the yaxis and therefore always have an xcoordinate of 0 


Term
For a parabola, the Axis of Symmetry always goes through ______. 

Definition
the vertex of the parabola 


Term
For a parabola, the equation of the Axis of Symmetry is always ___ = ____. 

Definition
x; xcoordinate of vertex 


Term
For a parabola, the range is always begins at the ______. 

Definition
ycoordinate of the vertex 


Term
True or False: For a parabola, the vertex is always the maximum point on the graph. 

Definition
False; sometimes that's true, but when it isn't, the vertex will be the minimum point of the graph 


Term
When solving for a variable in an equation, if you have to take the square root of both sides, you MUST then _____. 

Definition
assign a '+ or ' to the solution 


Term
In a polynomial equation, if you use factoring to solve it, you consequently set each factor equal to _____ and then solve _______. 

Definition


Term
When solving a system of equations, if you end up with an obviously false statement (i.e. 3=7), this is called a ________ and means ________. 

Definition
contradiction; there is no solution to the system of equations 


Term
When solving a system of equations, if you end up with an obviously true statement (i.e. 5=5), this is called an ________ and means ________. 

Definition
identity; there are infinitely many solutions since the two equations are the same thing 


Term
The Quadratic Formula will solve _____ quadratic equations. (a) some (b) none (c) all 

Definition


Term
The radicand of the Quadratic Equation is called the _________. 

Definition


Term
If the Discriminant is positive, this means _________. 

Definition
there are 2 realnumber solutions 


Term
If the Discriminant is negative, this means _________. 

Definition
there are no realnumber solutions 


Term
If the Discriminant is zero, this means _________. 

Definition
there is exactly 1 realnumber solution 


Term
A rational function is a function that can be expressed as a ______ and the denominator contains _______. 

Definition


Term
The denominator of a fraction can never equal _____. 

Definition


Term
For the function: f(x) = 3/(x4) the domain is _______. 

Definition
All numbers except 4 since plugging 4 in for x would cause the denominator to be zero. 


Term
For the function: f(x) = 7x/(x+3) the domain is _______. 

Definition
All numbers except 3 since plugging 3 in for x would cause the denominator to be zero. 


Term
For the function: f(x) = 19.5x/(2x6) the domain is _______. 

Definition
All numbers except 3 since plugging 3 in for x would cause the denominator to be zero. 


Term
For the function: f(x) = 8x/(5+2x) the domain is _______. 

Definition
All numbers except 2.5 since plugging 2.5 in for x would cause the denominator to be zero. 


Term
For the function: f(x) = 3/(x^24) the domain is _______. 

Definition
All numbers except 2 or 2 since plugging 2 or 2 in for x would cause the denominator to be zero. 


Term
When simplifying a rational expression, the first step is ALWAYS to ________ all numerators and denominators. 

Definition


Term
When getting common denominators for a pair of fractions, you always have to multiply the numerator and denominator of each individual fraction by the same thing. Why? 

Definition
So that, in effect, you are multiplying by the number 1. Therefore you're not changing the value of the fraction. 


Term
One way to rewrite the expression (2x3) is to write it as _______. 

Definition


Term
One way to rewrite the expression (4x7) is to write it as _______. 

Definition


Term
One way to rewrite the expression (x10) is to write it as _______. 

Definition


Term
When solving a rational equation, you should start by _______ both sides of the equation by the _____. This will ________. 

Definition
multiplying; LCD; get rid of all denominators (fractions) 


Term
An assumption is ____________. 

Definition
something not stated but taken as fact (i.e. Without reading the textbook, I will assume that it is accurate.) 


Term
A condition is ____________. 

Definition
a requirement or restriction (i.e. A condition for graduation is passing MATH 111.) 


Term
The word 'difference' means _______. 

Definition


Term
The word 'sum' means _______. 

Definition


Term
The word 'quotient' means _______. 

Definition


Term
The word 'product' means _______. 

Definition


Term
In word problems, the word 'of' usually means ______. 

Definition


Term
In the Order of Operations (PEMDAS), the P stands for ________. 

Definition
parentheses and all other grouping symbols (i.e. parentheses, brackets, braces, absolute values, square roots) 


Term
In the Order of Operations (PEMDAS), the E stands for ________. 

Definition


Term
In the Order of Operations (PEMDAS), the M stands for ________. 

Definition


Term
In the Order of Operations (PEMDAS), the D stands for ________. 

Definition


Term
In the Order of Operations (PEMDAS), the A stands for ________. 

Definition


Term
In the Order of Operations (PEMDAS), the S stands for ________. 

Definition


Term
When using the Order of Operations (PEMDAS) to simplify an expression, we simplify multiplications and divisions SIMULTANEOUSLY FROM _________. 

Definition


Term
When using the Order of Operations (PEMDAS) to simplify an expression, we simplify additions and subtractions SIMULTANEOUSLY FROM _________. 

Definition


Term
The 'input variable' is usually the variable ___. 

Definition


Term
The 'output variable' is usually the variable ___. 

Definition


Term
The 'independent variable' is usually the variable ___. 

Definition


Term
The 'dependent variable' is usually the variable ___. 

Definition


Term

Definition
False, it doesn't vary. It's a constant. It's always the same number, 3.14159... 


Term
When adding or subtracting, you must have ___________. 

Definition


Term
The initial value of a function is the function's _______. 

Definition


Term
When solving an equation for x, you can ALWAYS __________. 

Definition
set the left side of the equation to y1, set the right side of the equation to y1, and see where they intersect! 


Term
An 'identity' is ___________. 

Definition
something you can steal (just kidding),it's a statement that is obviously true (i.e. 3=3) 


Term
A 'contradiction' is _________. 

Definition
a statment that is obviously false (i.e., 5=7) 


Term
When you flip a fraction, you are finding the ___________. 

Definition


Term
Three main ways to write out the solution set to an inequality statement are: ______, ______, and ________. 

Definition
inequality notation; interval notation; line graph 


Term
When graphing a function on the calculator, you must first enter the function on the menu labeled ______. 

Definition
y= (i.e., top lefthand button on the calculator) 


Term
When graphing a function on the calculator, it is sometimes helpful to allow the calculator to select your ymin and ymax. To do this you must press _________. 

Definition


Term
When graphing a collection of individual points on the calculator, the easiest way to select an approrpiate viewing window is to press Zoom ______. 

Definition


Term
To find the intersection point(s) of two functions, you enter the functions on the ______ menu, make sure the two functions appear on the screen when you graph, then press ___, ___, ___, ___, ___, ___. 

Definition
y=; Second; Trace; 5; Enter; Enter; Enter 


Term
To enter individual points into the calculator you must press ____ and then _____. 

Definition


Term
To clear out a list of data (i.e., L1, L2,...), one way is to go to the lists, highlight the name of the list you wish to clear out and then press ____ and then _____. 

Definition


Term
To find the Line of Regression (i.e. Line of Best Fit), you enter your data with xvalues in ____ and yvalues in ____. Then, you would press ____, ____, ____, and _____ 5 times. 

Definition
L1; L2; Stat; Right Arrow; 4; Enter 


Term
To generate an inputoutput table on the calculator, you must first enter the function on the _____ menu and then press _____ and then ______. 

Definition


Term
When graphing a function, usually it is easiest to select an appropriate viewing widow by pressing Zoom ____. 

Definition


Term
To find the maximum value of a function using the calculator, you would go to Second Trace and select _______. 

Definition


Term
To find the minimum value of a function using the calculator, you would go to Second Trace and select _______. 

Definition


Term
When plotting individual points on the calculator you must first go to the y= menu and turn on _______. 

Definition


Term
On the calculator, the Absolute Value function is found by pressing _____, ______, _______. 

Definition


Term
On the calculator, the Inequality Symbols are found by pressing _____, ______. 

Definition


Term
When making a Line Graph to express an interval, a ___________ means you do NOT include that particular number in your solution. 

Definition


Term
When making a Line Graph to express an interval, a ___________ means you DO include that particular number in your solution. 

Definition
closed circle (i.e., a circle that is shaded in) 


Term
In Interval Notation, parentheses are the same as _______ circles on a line graph. 

Definition


Term
In Interval Notation, brackets (i.e., [,] )are the same as _______ circles on a line graph. 

Definition


Term
The symbol for inifinity looks like the number ___ laying down on its side. 

Definition


Term
In Interval Notation, infinity ALWAYS gets a _________ next to it. 

Definition


Term
T/F: In a function, each xvalue can be used one time, at most. 

Definition


Term
T/F: In a function, each yvalue can be used one time, at most. 

Definition


Term
For the function f(x)=5x7, f(2)=____. 

Definition


Term
For the function f(x)=5x7, f(3)=____. 

Definition


Term
For the function f(x)=5x7, f(Q)=____. 

Definition


Term
For the function f(x)=5x7, f(R+W)=____. 

Definition
5(R+W)7 (NOTE: this can be simplified using the Distributive Property) 


Term
In word problems that use the variable TIME, this variable is usually the label for the _______ axis. 

Definition


Term
If a function can be written in slopeintercept form, this means that _____________. 

Definition


Term
The units for the slope of a function are always the ______ divided by the ______. 

Definition
units for x; units for y (i.e., if x is time measured in hours and y is distance measured in miles, then the units of slope will me 'miles/hour'.) 


Term
To find slope of a line that passes through 2 given points, we would use the formula ________. 

Definition


Term
If a function can be written in slopeintercept form, this means that _____________. 

Definition
it's graph is a straight line 


Term
If a function has a slope of 0, this means its graph is a _______ line. 

Definition


Term
If the graph of an equation is a vertical line, then its slope is _________. 

Definition


Term
T/F: If two lines have the same slope they are guaranteed to be parallel. 

Definition
False; they must also have the added condition of 'different yintercepts' 


Term
T/F: Perpendicular lines sometimes have slopes that are the same sign. 

Definition
False; their slopes are ALWAYS oppositely signed (i.e., 2/3 and 3/2; 4/5 and 5/4; 17 and 1/17) 


Term
T/F: If two lines are perpendicular, then their slopes multiply to give 1. 

Definition
True (the only except is when considering a vertical line and a horizontal line) 


Term
On the calculator, when calculating the Line of Best Fit/Regression Line (using LinReg), the value for 'r' that the calculator gives you tells you ______. 

Definition
how good of a fit the Line of Best Fit is for your data points that you entered 


Term
T/F: If a function passes through the origin, then we know the yintercept and an xintercept. 

Definition


Term
A constant function has slope equal to _____. 

Definition


Term
A constant function only has one variable in the equation: ______. 

Definition


Term
T/F: The equation x=3 is a constant function. 

Definition
False; it's not a function (it doesn't pass the vertical line test), therefore it's not ANY kind of function! 


Term
In math the word 'rate' basically means _____. 

Definition


Term
In math the phrase'rate of change' basically means _____. 

Definition


Term
In math, the word 'rational' basically means _______. 

Definition
Fraction; after all, the first 5 letters of the word 'rational' form the word 'ratio' 


Term
A condition is ____________. 

Definition
a requirement or restriction (i.e. A condition for graduation is passing MATH 111.) 


Term
To write y in terms of x means to solve for ____. 

Definition


Term
To write x in terms of y means to solve for ____. 

Definition


Term
To write Q in terms of P means to solve for ____. 

Definition


Term
To write P in terms of Q means to solve for ____. 

Definition


Term
When solving a system of equations, the Substitution Method will work always/never/sometimes. 

Definition


Term
When solving a system of equations, the Elimination Method will work always/never/sometimes. 

Definition


Term
When solving a system of equations, the Graphing Method will work always/never/sometimes. 

Definition


Term
To solve a system of equations by Graphing, you must first __________ in both equations. 

Definition
isolate y (that way you can plug the equations into your calculator on the 'y=' menu) 


Term
In Quantity/Rate problems, a key word for numbers that are rates is ______. 

Definition
per (whenever you see 'per', you know the number is a 'rate') 


Term
In Quantity/Rate problems, the first thing to do is define _________. 

Definition
the categories (i.e. Indonesian Coffee & Honduran Coffee; An account that pays 5% interest & an account that pays 3%) 


Term
In Quantity/Rate tables, you ______ horizontally. 

Definition


Term
In Quantity/Rate tables, you ______ vertically. 

Definition
add (the exception is the 'rate' column) 


Term
In Quantity/Rate tables, the last entry in the 'rate' column will always be greater/smaller/between the other rates listed above. 

Definition
between (this is the average rate for the problem) 


Term
A quadratic function or equation is one in which the highest power of x is ___. 

Definition


Term
A linear function or equation is one in which the highest power of x is ___. 

Definition


Term
A cubic function or equation is one in which the highest power of x is ___. 

Definition


Term
A parabola is what you get when you graph a __________ function. 

Definition


Term
A straight line is what you get when you graph a __________ function. 

Definition


Term
xintercepts are found by setting ___ equal to zero. 

Definition


Term
yintercepts are found by setting ___ equal to zero. 

Definition


Term
The axis of symmetry of a parabola is the _______ line that passes through its _________. 

Definition


Term
The coordinates of the vertex of a parabola are denoted by the variables _____. 

Definition


Term
If a quadratic function opened up (vertex is a minimum point) and the vertex is (3,4), then the range would be_______. 

Definition
y greater than or equal to 4. 


Term
For a quadratic function opening down, the range is always ________. 

Definition
y less than or equal to k (the ycoordinate of the vertex) 


Term
If a quadratic function opened down (vertex is a minimum point) and the vertex is (3,4), then the range would be_______. 

Definition
y less than or equal to 4. 


Term
For quadratic functions, the domain is sometimes/always/never all real numbers. 

Definition


Term
When factoring a polynomial, the first factoring technique to try is always_______. 

Definition
GCF (i.e., for the polynomial 2x^24x+2, first factor out the GCF of 2, then try doing something else). 


Term
When Completing The Square, the quantity that you add to both sides, so that the left side factors nicely, is _______. 

Definition
(b/2)^2 (NOTE: the b used here is not necessarily the b from the original problem; the b used here is the coefficient of x AFTER dividing both sides of the equation by a, the coefficient of x^2) 


Term
When solving a quadratic polynomial equation, Completing The Square will work always/sometimes/never. 

Definition


Term
The first 2 steps of Completing The Square are always ____________ and ___________. 

Definition
Making sure the number c is on the opposite side of the equation as the other terms; dividing both sides of the equation by the number a (NOTE: it doesn't matter which of these 2 steps you do first) 


Term
Determine as many ways as you can to solve the given equation: 9x^281=0 

Definition
Factoring (box method) Factoring (difference of squares) Completing the Square Quadratic Formula Graphing Method (graph the left side as y1 and the right as y2 and see where they intersect) Add 81, divide by 9 and square root 


Term
When solving a quadratic polynomial equation, Completing The Square will work always/sometimes/never. 

Definition


Term
The first 2 steps of Completing The Square are always ____________ and ___________. 

Definition
Making sure the number c is on the opposite side of the equation as the other terms; dividing both sides of the equation by the number a (NOTE: it doesn't matter which of these 2 steps you do first) 


Term
Determine as many ways as you can to solve the given equation: 9x^281=0 

Definition
Factoring (box method) Factoring (difference of squares) Completing the Square Quadratic Formula Graphing Method (graph the left side as y1 and the right as y2 and see where they intersect) Add 81, divide by 9 and square root 


Term
The 'principal square root' of a number is ____________. 

Definition


Term
When taking the square root of both sides of an equation, you must ___________ 

Definition
determine BOTH the positive AND the negative square roots. 


Term
The square root of a fraction can be interpreted as the square root of the __________ divided by the square root of the ____________. 

Definition


Term
Whatever is inside the square root symbol is called the _____________. 

Definition


Term
That small number that is immediately left of a radical sign is called the ____________ of the radical. 

Definition


Term
In a fraction, before you can 'cancel' something between the top and the bottom of the fraction, you must first be able to _______________. 

Definition
factor that thing out of BOTH the top and bottom of the fraction 


Term
Depending on what quadratic equation you're trying to solve, some of the methods for solving it might be: _________. 

Definition
quadratic formula factoring solving by taking square roots graphing completing the square 


Term
T/F: The radius of a circle is twice the diameter. 

Definition
False; that statement is backwards (i.e. D = 2R) 


Term
The main characteristic of an 'equilateral triangle' is that _________________. 

Definition
its sides are all the same length 


Term
The main characteristic of an 'isosceles triangle' is that _________________. 

Definition
exactly 2 sides are the same length 


Term
The main characteristic of a 'right triangle' is that _________________. 

Definition
one of the angles is 90 degrees 


Term
An object in 'freefall' is affected only by _____________. 

Definition


Term
When completing the square to solve a quadratic equation, you must add _____ to both sides. 

Definition


Term
For a quadratic function (i.e. f(x)=3x^24x+7), to determine the vertex by hand you must _________________. 

Definition
find b/(2a) to get the xcoordinate and then plug that number into the function to get the ycoordinate 


Term
The imaginary number i is equal to ______. 

Definition


Term

Definition


Term

Definition


Term

Definition


Term

Definition


Term
The complex conjugate of 35i is _____. 

Definition


Term
The complex conjugate of 45i is _____. 

Definition


Term
The complex conjugate of 3+5i is _____. 

Definition


Term
The word 'discriminant' makes reference to ________ 

Definition
b^24ac (i.e. the radicand in the quadratic formula) 


Term
Is learning all this math useful? 

Definition
Yes, among other things it will help to develop your mental faculties and it teaches clear thinking 


Term
The vertex of the function y=4(x5)^2+7 is _______. 

Definition


Term
The vertex of the function y=4(x+5)^2+7 is _______. 

Definition


Term

Definition


Term

Definition


Term
T/F: In ALL cases, the degree of a polynomial equation determines how many solutions there will be. 

Definition
True, although sometimes it's VERY difficult to find all of them 


Term
When changing a quantity from one set of units to another (i.e. change 55 mph into ft/sec), you must ALWAYS multiply by a fraction whose numerator and denominator are _______. 

Definition


Term
A _______ is an equation wherein there is a single fraction equal to a single fraction. 

Definition


Term
The basic formula for 'direct variation' is _____________. 

Definition


Term
The basic formula for 'inverse variation' is _____________. 

Definition


Term
In variation problems, the 'k' is called the _______________. 

Definition
constant of propotionality 


Term
No matter what 'a' is (except 0), the fraction a/a can always be simplified to ____. 

Definition


Term
T/F: (a/b) = (a)/b = a/(b) 

Definition
True, it doesn't matter where you put that single minus sign. 


Term
When dividing 1 rational expression by another, the first thing to do is ________. 

Definition
rewrite the problem using multiplication 


Term
One way to determine if a certain polynomial is a factor of the other is to divide the first polynomial into the second and then check to see if _______. 

Definition
the remainder is 0 (in that case we would say the first polynomial IS a factor of the second) 


Term
When solving an EQUATION that contains fractions, first determine the _____, then _______ both sides of the equation by it to clear remove all denominators. 

Definition


Term

Definition


Term

Definition
1 (since (ab)/(ba)= 1(ba)/(ba) in which case the 2 factors of (ba) both cancel and 1 is all that is left over) 


Term
When adding and subtracting ANY fractions you must first get ______. 

Definition


Term
T/F: When multiplying fractions you must first get common denominators. 

Definition


Term

Definition


Term
Restrictions on the variable in an equation are primarily found in 2 ways. The first is to set the ________ equal to zero and solve. The second is to determine what makes the radicand _______. 

Definition
denominator; less than zero 


Term
Written with a positive exponent, (3/2)^2 = _____. 

Definition


Term
Written with a positive exponent, (5/4)^3 = _____. 

Definition


Term
Written with a positive exponent, 3/2^2 = _____. 

Definition
3*2^2 = 3*4 = 12 (Notice that in the original problem, only the 2 was being raised to a negative power; the 3 was not) 


Term
Written with a negative exponent, (3/2)^2 = _____. 

Definition


Term
A number in scientific notation ALWAYS has ____ digit(s) to the left of the decimal point. 

Definition


Term
In scientific notation, the exponent (on the 10) tells you ________ if you were to convert the number to standard decimal notation. 

Definition
how many places to move the decimal point 


Term
In the formula for Compound Interest, the variable n represents _________. 

Definition
the number of compounding periods in a single year 


Term
If interest is compounded monthly, then n = ____. 

Definition


Term
If interest is compounded weekly, then n = ____. 

Definition


Term
If interest is compounded semiannually, then n = ____. 

Definition


Term
If interest is compounded quarterly, then n = ____. 

Definition


Term
If interest is compounded annually, then n = ____. 

Definition


Term
If interest is compounded daily, then n = ____. 

Definition


Term
If interest is compounded semimonthly, then n = ____. 

Definition


Term
For a rational (fraction) exponent, the denominator tells you _________. 

Definition
the index of the radical (what root to take) 


Term
If you're taking an even root (square root, 4th root, 6th root, etc.) of a negative number, the answer will always be ________. 

Definition


Term
If you're taking an odd root (3rd root, 5th root, etc.) of a negative number, the answer will always be ________. 

Definition


Term
When adding or subtracting radicals, the radicals MUST have the same _____ and the same ______. 

Definition
index; radicand (i.e. they must be the EXACT SAME radicals) 


Term
For a function f(x), if f(3)=8 then for the inverse function g, g(8)=___. 

Definition


Term
For a function f(x), if f(6)=2 then for the inverse function g, g(2)=___. 

Definition


Term
If you're given a sequence of numbers (i.e. 1,1,2,3,5,8,...) and asked to form an inputoutput table, the inputs will be the ______. 

Definition
the natural numbers (1,2,3,4,5,6,...) 


Term
Exponential functions ALWAYS have _________ asymptotes. 

Definition


Term
The domain for exponential functions is ________. 

Definition


Term
The range for exponential functions of the form f(x)=b^x is________. 

Definition


Term
TRUE/FALSE: Exponential functions sometimes have vertical asymptotes. 

Definition


Term
TRUE/FALSE: Exponential functions always have horizontal asymptotes. 

Definition


Term
On the calculator, the LOG button means 'log base____'. 

Definition


Term
On the calculator, the LN button means 'log base____'. 

Definition


Term
If you're having trouble solving an equation which is in 'log form', it will probably help to convert it to _________. 

Definition


Term
If you're having trouble solving an equation which is in 'exponential form', it will probably help to convert it to _________. 

Definition


Term

Definition


Term

Definition


Term

Definition


Term

Definition
log(3x4) (this does not simplify!) 


Term
The equation S=Pe^(rt) is used to determine interest compounded _________. 

Definition


Term
e is approximately equal to ____. 

Definition


Term
The Average Rate of Change of a function between 2 specific points is ________. 

Definition
the SLOPE of the STRAIGHT line connecting the 2 points 


Term
When looking at the graph of a function, the 'Rate of Change' is ________. 

Definition


Term
An exponential function is a function that has the _____ in the ______. 

Definition
independent variable (usually x or t); exponent 


Term
Problems involving radioactive elements are always examples of exponential _______. 

Definition


Term
There are 2 ways of setting up an exponential function. You can either use the _______ equation or the y=Ce^(rt) equation. 

Definition


Term
There are 2 ways of setting up an exponential function. You can either use the _______ equation or the y=Ca^t equation. 

Definition


Term
If the Percentage Rate of Change is constant for a function then that function is an ___________ function. 

Definition


Term
The Growth/Decay Factor of an exponential function is denoted by the variable ____. 

Definition


Term
The Growth/Decay Rate of an exponential function is denoted by the variable ____. 

Definition


Term
The Percentage Rate of Change of an exponential function is found by _____________. 

Definition
writing the growth/decay rate r AS A PERCENT. 


Term
The Growth/Decay Rate of an exponential function is found by _____________. 

Definition
subtracting 1 from the Growth/Decay Rate 'a' 


Term
Adding 1 to the Growth/Decay Rate r gives _________. 

Definition
the Growth/Decay Factor 'a' 


Term
If the Growth/Decay Factor 'a' of an exponential function is greater than 1, this means ___________. 

Definition
the function has exponential GROWTH 


Term
If the Growth/Decay Factor 'a' of an exponential function is less than 1, this means ___________. 

Definition
the function has exponential DECAY 


Term
If 'a' denotes the oneyear Growth Factor of an exponential function then ______ denotes the 5year Growth Factor. 

Definition


Term
When the finding the inverse of a function you need to _____________ and then ____________. 

Definition
switch the x's and y's; solve for y 


Term
T/F: If something is raised to a negative power, the answer will be negative. 

Definition
False (negative signs in exponents have nothing to do with the sign of the answer) 

