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2-Precalculus:Homework:2.5:Notes
2-Precalculus:Homework:2.5:Notes
34
Mathematics
Undergraduate 1
02/15/2016

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Term
When determining intervals on which the function is increasing or decreasing the interval is based on what value?
Definition
The "x" value where the interval begins/ends increasing, decreasing, or stays constant.
Term
If there are multiple intervals, where a function is(increasing/decreasing/constant) what do you do?
Definition
Use union symbols to represent intersections.
Term
What is the domain?
Definition
The interval of "x" values
Term
What is the range?
Definition
The interval of "y" values
Term
What is an interval?
Definition
[Lowest Value, Highest Value]
Term
Intervals at solid points are included, while intervals at holes are?
Definition
Excluded
Term
What is Slope Formula?
(x1,y1) (x2,y2)
Definition
((y2-y1)/(x2-x1))=Slope
Term
What is Slope Formula?
(A,B) (C,D)
Definition
((D-B)/(C-A))=Slope
Term
How do you find x-intercept when given a graph?
Definition
1.)Pick two points on a line that crosses the x-axis:
(A,B) (C,D)
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2.)Use Slope Formula to Calculate Slope
((D-B)/(C-A))=Slope
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3.)Put it in Point Slope Form
(y-D)=(Slope)(x-C)
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4.)Set it in slope intercept form by setting the Point-Slope form equal to "y".
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5.)Set "y" equal to zero and solve for "x".
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Term
What is Slope Intercept Form?
Definition
y=(Slope)x+(y-intercept)
Term
What is Point Slope Form?
(A,B) (C,D)
Definition
(y-D)=(Slope)(x-C)
Term
What is Point Slope Form?
(x1,x2) (y1,y2)
Definition
y-y2=(Slope)(x-x2)
Term
What is (A/B)*C?
Definition
(AC/B)
Term
What is (A/B)+(C/D)?
Definition
(AD/BD)+(AC/BD)
Term
What is (A/B)-(C/D)?
Definition
(AD/BD)-(AC/BD)
Term
What is (A/B)/(C/D)?
Definition
1.)(A/B)*(D/C)
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2.)(AD/BC)
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Term
How do you find y-intercept when given a graph?
Definition
1.)Pick two points on a line that crosses the x-axis:
(A,B) (C,D)
---
2.)Use Slope Formula to Calculate Slope
((D-B)/(C-A))=Slope
---
3.)Put it in Point Slope Form
(y-D)=(Slope)(x-C)
---
4.)Set it in slope intercept form by setting the Point-Slope form equal to "y".
---
5.)Set "x" equal to zero and solve for "y".
---
Term
When is a graph positive?
Definition
When a line rises from left to right.
Term
When is a graph negative?
Definition
When a line falls from left to right.
Term
When is a graph neither negative or positive?
Definition
When a line is constant.
Term
If a curve does not touch the "y" axis the it does not have a what?
Definition
y-intercept
Term
If a curve does not touch the "x" axis the it does not have a what?
Definition
x-intercept
Term
What is the x-intercept?
Definition
Where the graph crosses the x-axis
Term
What is the y-intercept?
Definition
Where the graph crosses the y-axis
Term
What is a y-intercept like?
Definition
(0,A)
Term
What is a x-intercept like?
Definition
(A,0)
Term
How does one calculate average rate of change?
Definition
Difference Quotient of the Form
Term
What is the Difference Quotient of the Form?
Definition
(f(b)-f(a)/(b-a)
Term
How do you find the Difference Quotient of a problem of this Form?
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Problem:
f(x)=Cx^2+x,a=D
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Difference Quotient
(f(x)-f(a)/(x-a)
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Definition
(Cx)+(-f(a))/-a)
Term
How do you find the difference quotient of a problem of this form?
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Difference Quotient:
((f(x+h)-(f(x))/h
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Problem:
f(x)=(Ax^2)+Bx+C
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Definition
1.)Solve the problem by plugging in the function and completing the proper calculations.
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Term
What function would represent the volume of a box made from a piece of sheet metal that is "A" centimeters by "A". With the square corners cut out so that the sides can be folded up to make a box. Letting "x" represent the length of a cut-out square?
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Definition
1.)This is the function...
V=x(A-2x)(A-2x)
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Term
What is the domain of a box made from a piece of sheet metal that is "A" centimeters by "A". With the square corners cut out so that the sides can be folded up to make a box. Letting "x" represent the length of a cut-out square?
---
Definition
1.)The domain is...
0---
Term
What is the graph of a box made from a piece of sheet metal that is "A" centimeters by "A". With the square corners cut out so that the sides can be folded up to make a box. Letting "x" represent the length of a cut-out square?
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Definition
1.)An Arch
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Term
What is the maximum value of a box made from a piece of sheet metal that is "A" centimeters by "A". With the square corners cut out so that the sides can be folded up to make a box. Letting "x" represent the length of a cut-out square?
---
Definition
1.)You can guess it, it's not all three the same number, and the numbers don't feel that related to the function.
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