Term
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Definition
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Term
| T/F A natural number is and integer. |
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Definition
| True. It may be either positive or negative. |
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Term
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Definition
| the ratio of two integers |
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Term
| T/F A common factor is one integer divided by another. |
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Definition
| False. A common fraction is one integer divided by another. The fraction can be either positive or negative. |
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Term
|
Definition
any positive or negative integer, or fraction made up
of integers |
|
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Term
| T/F Factorials are those which can be represented by the ratio of two integers |
|
Definition
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Term
|
Definition
positive and negative numbers which cannot be represented as
the ratio of two integers, e.g. 21/2 , 71/3, π (since π is not exactly 22/7). |
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Term
|
Definition
is that system of numbers which includes all
positive and negative rational and irrational numbers and the number 0. |
|
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Term
| -infinity...-4, -3, -2, -1,0,1,2,3,4...infinity+ |
|
Definition
| graphical representation of the real number system, a series of numbers that runs without end |
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Term
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Definition
| symbols which represent specific numbers, e.g. 1,6,-3/5. |
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Term
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Definition
| letters which represent or stand for explicit numbers |
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Term
| also known as a general number |
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Definition
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Term
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Definition
| a symbol which is used to represent different numbers throughout a particular discussion |
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Term
| T/F letters from the latter portion of the alphabet are utilized as variables |
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Definition
|
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Term
| T/F variables are explicit numbers that may have several values. |
|
Definition
| False. Variables are literal numbers that may have several values |
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Term
|
Definition
| symbol which represents the same number during a discussion |
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Term
| T/F a constant never changes its value |
|
Definition
| False. An absolute constant never changes its value and it usually is an explicit number such as 2, 1/3, etc. |
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Term
|
Definition
will have the same value throughout any one discussion or exercise, but may be
assigned different values in different exercises, and is normally represented by a literal number |
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Term
| The first few letters of the alphabet are conventionally used for these. |
|
Definition
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Term
|
Definition
The length of a line on a number scale which represents a
certain number, without regard to the direction (negative or positive) of the number from zero |
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Term
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Definition
| means the absolute value of x and equals x |
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Term
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Definition
| means the absolute value of 3 and equals 3. |
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Term
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Definition
| means the absolute value of -4 and equals 4. |
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Term
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Definition
| means the absolute value of 4 and equals –4. |
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Term
| The algebraic value of a number is |
|
Definition
equal to its distance and direction, either plus of minus, from a zero point
origin. |
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Term
|
Definition
combination of explicit and literal numbers
linked by the four symbols of fundamental mathematical operations; which are addition, subtraction,
multiplication, and division |
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Term
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Definition
|
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Term
|
Definition
| a distinct part of an algebraic expression which is separated from the rest of the expression by a plus or a minus sign, which is itself a part of the term |
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Term
| A + B –5D +6/F which are algebraic terms? |
|
Definition
| A(or +A), +B, -5D, and +6/F |
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Term
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Definition
| algebraic expression with only one term in it. |
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Term
|
Definition
| algebraic expression with two terms in it. |
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Term
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Definition
| an algebraic expression with three terms in it. |
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Term
|
Definition
| any algebraic expression containing more than one term, |
|
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Term
| What is the generic definition of a polynomial? |
|
Definition
| an expression which is composed of a term or terms that contain a literal number raised to a positive, integral number or zero power |
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Term
| T/F Expressions with terms containing literal numbers raised to a negative or a fractional power are generally excluded from the term polynomial. |
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Definition
|
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Term
| 3x2 + 5x + 5 is defined by? |
|
Definition
| restricted definition of a polynomial |
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Term
|
Definition
| part of an algebraic term which is multiplied by another part or parts of the same term |
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Term
| T/F an algebraic factor can be made up of more than one number. |
|
Definition
False. It can be made up of only one number which cannot be further broken down into integral, rational
numbers other than a combination of itself and the number 1 or its negative and the number –1 |
|
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Term
|
Definition
made up of only one number which cannot be further broken down into integral, rational
numbers other than a combination of itself and the number 1 or its negative and the number –1 |
|
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Term
| T/F an algebraic factor can be made up of several factors multiplied together |
|
Definition
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Term
| 7bTV, name all of the factors |
|
Definition
| 7 (a prime factor), b, T, V, 7b, 7bT, bT, bTV, 7T, 7TV, TV |
|
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Term
|
Definition
| factor by which the other factors of a term are multiplied |
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Term
|
Definition
| The explicit number part of the factor |
|
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Term
| T/F The factor normally considered as the coefficient is the factor listed first in the term |
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Definition
|
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Term
|
Definition
| the sum of two numbers is the same regardless of the order in which we add the numbers. That is, a + b is exactly the same as b + a. |
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Term
| a + b is exactly the same as b + a |
|
Definition
|
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Term
|
Definition
| sum of three or more numbers is the same regardless of how they are grouped. That is (a + b) + c is the same as a + (b + c) or c + a + b |
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Term
| (a + b) + c is the same as a + (b + c) or c + a + b |
|
Definition
|
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Term
|
Definition
| the product of two numbers is the same regardless of the order in which they are multiplied. That is, a times b is exactly the same as b times a. |
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Term
| a times b is exactly the same as b times a |
|
Definition
| commutative law for multiplication |
|
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Term
| associative law for multiplication |
|
Definition
| the product of three or more numbers is the same regardless of the order of multiplying the numbers together |
|
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Term
|
Definition
the product of a number and a sum of numbers is the
same as the sum of the products obtained by multiplying each of the other numbers by the first number. |
|
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Term
|
Definition
| the number which is multiplied by another number is known as the |
|
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Term
| number that we multiply by is called |
|
Definition
|
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Term
| the result of multiplying the multiplicand by the multiplier |
|
Definition
|
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Term
| the number which is divided into another number |
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
| n factorial or factorial n |
|
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Term
| sum of the variables of which asubn is the representative |
|
Definition
|
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Term
|
Definition
|
|
Term
|
Definition
|
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Term
|
Definition
|
|
Term
| The student must constantly remind himself that the a’s, b’s, x’s and y’s are literal numbers representing |
|
Definition
|
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Term
| we say that any number divided by 0 is |
|
Definition
|
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Term
|
Definition
| b is the base of the exponential expression |
|
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Term
|
Definition
| 3 is the power to which the base is raised |
|
|
Term
| If a letter or number appears without an exponent, |
|
Definition
| then the exponent is taken to be 1 |
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Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
|
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Term
| When we multiply x by x we arrive at the answer |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| T/F When we multiply like terms, we simply add the exponents of each of the terms and place it as the exponent of the original term |
|
Definition
|
|
Term
| what happens when our terms to be multiplied contain numerical coefficients |
|
Definition
multiplying the numerical coefficients together and going
through the same drill that we went through above with the letters and their exponents Thus: 6a2 * 3a3 = 18a5 |
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Term
|
Definition
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|
Term
|
Definition
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|
Term
|
Definition
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|
Term
|
Definition
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|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
|
|
Term
| 20x – 10x + 20y – 15y – 5x – 5y= |
|
Definition
|
|
Term
| –5xy + 10 – 5yx –5 + 15xy = |
|
Definition
|
|
Term
| 10 – 3a2b3c – 8 + 4b3a2c = |
|
Definition
|
|
Term
| 10a – (5a + 2b) + 3b – (2a-b) = |
|
Definition
|
|
Term
|
Definition
|
|
Term
| a – b + c – (3c – 2b – 2c)= |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
| the set of all x such that x is less than 5 |
|
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Term
|
Definition
|
|
Term
|
Definition
| largest value on box and whisker plot |
|
|
Term
| Left side of box on box and whisker plot |
|
Definition
| 1st quartile or 25th percentile |
|
|
Term
| Right side of box and whiskers plot |
|
Definition
| 3rd quartile or 75% percentile |
|
|
Term
| what is on the horizontal axis of a box and whiskers plot? |
|
Definition
|
|
Term
| what does a box and whiskers chart provide |
|
Definition
| a distribution of a data set based on the median and data quartiles |
|
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Term
|
Definition
| PERCENTILE.INC - k is in the range of 0 to 1 with 0 and 1 included. |
|
|
Term
| what are the two percentile functions in excel? |
|
Definition
| PERCENTILE.EXC and PERCENTILE.INC |
|
|
Term
| How do you interpret a result of 2.75 on the k = 0.25 percentile? |
|
Definition
| The second number in the ordered list of data represents the 25% percentile, and it's closer to 3 than 2. |
|
|
Term
| What is a data prerequisite for calculating a percentile? |
|
Definition
| the data must be in order from lowest to highest, ascending. |
|
|
Term
| if a data set is shown to have more than 3 modes what is generally said about that data set? |
|
Definition
|
|
Term
| what is a simple definition of the arithmetic mean? |
|
Definition
| the balance point in a distribution where the sum of deviations is equal to 0 |
|
|
Term
| T/F In the context of regression analysis, when the sum of the residuals is greater than zero, the data set is nonlinear. |
|
Definition
| False. The sum of the residuals is always zero, whether the data set is linear or nonlinear. |
|
|
Term
| T/F A random pattern of residuals supports a linear model. |
|
Definition
|
|
Term
| T/F A random pattern of residuals supports a non-linear model. |
|
Definition
| False. A random pattern of residuals supports a linear model |
|
|
Term
|
Definition
| Residual = Observed value - Predicted value |
|
|
Term
| T/F Each data point has one residual. |
|
Definition
|
|
Term
| A graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis |
|
Definition
|
|
Term
| What is plotted on the horizontal axis of a residual plot? |
|
Definition
| the independent variable, y |
|
|
Term
| What is plotted on the vertical axis of a residual plot? |
|
Definition
|
|
Term
| How do you assess the appropriateness of linear regression for your data? |
|
Definition
| Because a linear regression model is not always appropriate for the data, you should assess the appropriateness of the model by defining residuals and examining residual plots. |
|
|
Term
|
Definition
| shape of a residual plot for data that is not appropriate for linear regression |
|
|
Term
|
Definition
| shape of a residual plot for data that is not suitable for linear regression. |
|
|
Term
|
Definition
| the residual is the error in prediction |
|
|
Term
| Is linear regression appropriate? |
|
Definition
|
|
Term
| In mathematics, an ____ _____ is a function of one variable which is the composition of a finite number of arithmetic operations (+ – × ÷), exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of nth roots). |
|
Definition
|
|
Term
| T/F The elementary functions include the trigonometric and hyperbolic functions and their inverses, as they are not expressible with complex exponentials and logarithms. |
|
Definition
| False, they are expressible with complex exponentials and logarithms |
|
|
Term
| It follows directly from the definition for and elementary function that the set of elementary functions is closed under arithmetic operations and composition. It is also closed under differentiation. It is not closed under _____ and _______ _______. |
|
Definition
|
|
Term
| Elementary functions are ______ at all but a finite number of points. |
|
Definition
|
|
Term
| T/F Some elementary functions, such as roots, logarithms, or inverse trigonometric functions, are not entire functions and may be multivalued. |
|
Definition
| True, in physics, multivalued functions play an increasingly important role. They form the mathematical basis for Dirac's magnetic monopoles, for the theory of defects in crystals and the resulting plasticity of materials, for vortices in superfluids and superconductors, and for phase transitions in these systems, for instance melting and quark confinement. They are the origin of gauge field structures in many branches of physics. |
|
|
Term
| What are two special types of transcendental extensions within the field of rational functions? |
|
Definition
| the logarithm and the exponential |
|
|
Term
| Elements that are not algebraic are called _______. |
|
Definition
|
|
Term
| Wikis list of two types of elementary functions |
|
Definition
| Algebraic Functions and Elementary Transcendental Functions |
|
|
Term
| Functions that can be expressed as the solution of a polynomial equation with integer coefficients. |
|
Definition
|
|
Term
| These types of elementary functions are not algebraic. |
|
Definition
| Elementary Transcendental Functions |
|
|
Term
| Wikis list of three types of algebraic functions. |
|
Definition
| Polynomials, Rational Functions, Nth root |
|
|
Term
| _______ can be generated by addition, multiplication, and exponentiation alone. |
|
Definition
|
|
Term
| A polynomial of degree zero. |
|
Definition
|
|
Term
| T/F the graph of a horizontal straight line is a polynomial of degree zero. |
|
Definition
| True and it is called a constant function. |
|
|
Term
| T/F Zero degree polynomials are straight lines. |
|
Definition
| False, zero degree polynomials are HORIZONTAL straight lines, first degree polynomials are graphed as a straight line. |
|
|
Term
| A second degree polynomial is graphed as a _______. |
|
Definition
|
|
Term
| What is another name for a second degree polynomial? |
|
Definition
|
|
Term
|
Definition
| a third degree polynomial |
|
|
Term
| What do you call a 4th degree polynomial function? |
|
Definition
|
|
Term
| What do you call a 5th degree polynomial function? |
|
Definition
|
|
Term
| What do you call a 6th degree polynomial function? |
|
Definition
|
|
Term
| A ratio of two polynomials. |
|
Definition
|
|
Term
| Yields a number whose square is the given one x^1/2. |
|
Definition
|
|
Term
| Yields a number whose cube is the given one x^1/3 |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
The Nth root of a number x, is a number r which, when raised to the power n yields x.
r^{n}=x, where n = 1 or a first degree root. |
|
|
Term
| A real number has n ____ of degree ___. |
|
Definition
|
|
Term
| A complex number has ____ roots of degree n. |
|
Definition
|
|
Term
| T/F The roots of zero are distinct. |
|
Definition
| False, the roots of 0 are not distinct, they all equal 0. |
|
|
Term
| The n nth roots of any real or complex number (except 0) are all ______. |
|
Definition
|
|
Term
| Nth Root Rule 1 of 4 - If n is even and x is real and positive, then... |
|
Definition
| one of its nth roots is positive, one is negative, and the rest are either non-existent or complex, but not real. |
|
|
Term
| Nth Root Rule 2 of 4 - If n is even and x is real and negative, then... |
|
Definition
| none of the nth roots is real |
|
|
Term
| Nth Root Rule 3 of 4 - If n is odd and x is real, then... |
|
Definition
| one nth root is real and has the same sign as x, while other roots are not real |
|
|
Term
| Nth Root Rule 4 of 4 - If x is not real, then.... |
|
Definition
| none of its nth roots is real |
|
|
Term
| T/F The radical symbol denotes a function. |
|
Definition
|
|
Term
| In calculus, _____ are treated as special cases of exponentiations, where the exponent is a ______. |
|
Definition
|
|
Term
| Roots are particularly important in the theory of ____ ____. |
|
Definition
|
|
Term
| The _____ ______ determines the radius of convergence of a power series. |
|
Definition
|
|
Term
| Every positive real number x has a single positive nth root called the _______ ____ ______. |
|
Definition
|
|
Term
| T/F The nth roots of almost all numbers are irrational. |
|
Definition
|
|
Term
|
Definition
| Shows the four 4th roots of -1, none of which is real. If it's not on the line, it's not an integer and therefore is not real (?) |
|
|
Term
|
Definition
| The three 3rd roots of -1, one of which is a negative real number. |
|
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Term
|
Definition
| The graph of y equal to plus or minus the square root of x. |
|
|
Term
|
Definition
| The graph of y is equal to the cube root of x. |
|
|
Term
|
Definition
The square roots of i.
The two square roots of a complex number are always negatives of each other. For example, the square roots of -4 are 2i and -2i, and the square roots of i are ...
1 over the square root of 2*(one +i) AND negative 1 over the square root of 2*(one + i).
If we express a complex number in a polar form, then the square root can be obtained by taking the square root of the radius (r) and halving the angle. |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| In dimensional analysis, transcendental functions are notable because they make sense only when their argument is _______. |
|
Definition
|
|
Term
| T/F applying a non-algebraic operation to a dimension creates a meaningless results. |
|
Definition
|
|
Term
| Raises a fixed number to a variable power. |
|
Definition
|
|
Term
| Formally similar to trigonometric functions |
|
Definition
|
|
Term
| The inverses of exponential functions. |
|
Definition
|
|
Term
| Raises a variable number to a fixed power. |
|
Definition
|
|
Term
| Also known as Allometric Functions |
|
Definition
|
|
Term
| Describe periodic phenomena. |
|
Definition
|
|
Term
| What are the 5 types of transcendental functions? |
|
Definition
| exponential, hyperbolic, logarithms, power functions, and periodic functions |
|
|
Term
|
Definition
| In mathematics, an exponential function in this form in which the input variable x occurs as an exponent. |
|
|
Term
|
Definition
| The natural exponential function of y equals the letter e to the power of x |
|
|
Term
|
Definition
| A function of the form f(x) = b to the power of x + c is also considered an exponential function |
|
|
Term
| What is the representation of an exponential function? |
|
Definition
| the letter e raised to the power of x |
|
|
Term
| What is the inverse of the exponential function? |
|
Definition
|
|
Term
| What is the derivative of the exponential function? |
|
Definition
| the derivative of the exponential function IS itself or the letter e raised to the power of x |
|
|
Term
| What is the indefinite integral of the exponential function? |
|
Definition
| the letter e to the power of x plus the constant, C |
|
|
Term
| What are examples of common applications for the exponential function? |
|
Definition
| compound interest, Euler's Identity, Euler's Formula, half-lives, exponential growth, exponential decay |
|
|
Term
| The exponential function arises whenever a quantity grows or decays at a rate _______ to its _______ _________. |
|
Definition
| proportional, current value |
|
|
Term
| What is the exponentiation identity? |
|
Definition
| exp(x + y) = exp(x) * exp(y) |
|
|
Term
| The exponential function extends to an _____ ______ on the _____ _____. |
|
Definition
| entire function, complex plane |
|
|
Term
| Euler's formula relates its values at purely ______ ______ to trigonometric functions. |
|
Definition
|
|
Term
| T/F The exponential function has analogues for which the argument is a matrix. |
|
Definition
|
|
Term
| The importance of the exponential function in mathematics and the sciences stems mainly from properties of its ________. |
|
Definition
|
|
Term
| What is the derivative of the letter e to the x power? |
|
Definition
| d over dx time the letter e to the power of x. |
|
|
Term
|
Definition
| In mathematics, a constant function is a function whose (output) value is the same for every input value.[1][2][3] For example, the function y(x)=4 is a constant function because the value of y(x) is 4 regardless of the input value x (see image). |
|
|
Term
|
Definition
In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero).
When the function is of only one variable, it is of the form f(x)=ax+b, where a and b are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. a is frequently referred to as the slope of the line, and b as the intercept. |
|
|
Term
|
Definition
In linear algebra, a linear function is a map f between two vector spaces that preserves vector addition and scalar multiplication:
f(x + y)= f(x) + f(y)
f(a) = af(x).
Here a denotes a constant belonging to some field K of scalars (for example, the real numbers) and x and y are elements of a vector space, which might be K itself. |
|
|
Term
| N = x(10 raised to the power of c), where 1<= x <10 and c is an integer. |
|
Definition
|
|
Term
| T/F scientific notation uses logarithms to the base 10 called complex logarithms. |
|
Definition
| False scientific notation uses logarithms to the based 10 called common logarithms. |
|
|
Term
| square and cube root of 100 = |
|
Definition
|
|
Term
| square and cube root of 110 equals |
|
Definition
|
|
Term
| square and cube root of 196 equals |
|
Definition
|
|
Term
| square and cube root of 169 equals |
|
Definition
|
|
Term
| square and cube root of 84 equals |
|
Definition
|
|
Term
| square and cube root of 64 equals |
|
Definition
|
|
Term
| square and cube root of 16 equals |
|
Definition
|
|
Term
| square and cube root of 30 equals |
|
Definition
|
|
Term
| square and cube root of 50 equals |
|
Definition
|
|
Term
| square and cube root of 60 equals |
|
Definition
|
|
Term
| square and cube root of 70 equals |
|
Definition
|
|
Term
| square and cube root of 80 equals |
|
Definition
|
|
Term
| square and cube root of 90 equals |
|
Definition
|
|
Term
| square and cube root of 190 equals |
|
Definition
|
|
