Kinds of Functions
Translation/Dilation of Functions
Composition of Functions
Inverse Function
Reflection/Absolute
100
Given that f(x)=2x + 5 Name the type of function this is.
Linear Function
100
If the original Function is f(x)=x^2 and then G(x)=x^2 + 4.Describe the change between F(x) and G(x).
Vertical Translation by four units
100
F(x)=2x +3 and G(x)= √(x-2), then what is the value of F(G(3))
F(G(3))= 5
100
What is a function called when the inverse of that function is also a function?
Invertible
100
What is necessary for a function to be even?
The function must have all even exponents
200
Given that F(x)=2x^3 + 5 what type of Function is this?
Polynomial Function
200
If y=F(X) , then describe y=3F(x)
Vertical dilation by 3 units
200
If G(x)= lx + 2l - 3 and F(x)= x^2 -4, then give the equation of G(F(x)) in terms of x
G(F(x))= lx^2 - 2l -3
200
What are strictly increasing or decreasing functions called?
One-to-one functions
200
What property do odd functions have?
Rotational symmetry around the origin
300
Given a Relation: {(1,2), (3,4), (4,5), (1,3)} Tell us whether or not this is a Function. Why?
No It fails the vertical line test..
300
What would the new equation be if you dilate y=F(x) by 5 horizontally and by 7 vertically.
y=7F(x/5)
300
If F(x)= x^2 and G(x)= 2x - 3, and F(G(x))=1, then what is x?
x= 1, 2
300
When in parametric mode, what would you enter when trying to graph function f(x)=3x+8 and its inverse?
X1T=T Y1T=3T+8 X2T=3T+8 Y2T=T
300
What transformation is needed to reflect a function over the x axis?
A vertical dilation of -1
400
Given the Function: f(x)= 2^x +78 tell us what type of Function this is.
This is an exponential Function
400
If y=F(X) , then describe the transformation y= 2F(3x)
Vertical Dilation by 2 units and Horizontal dilation by 1/3 of a unit...
400
If F(G(x))= (x-3)^2 and F(x)= x^2, then what is G(x)=?
G(x)=x-3
400
What is the equation for the inverse of function f(x)=7x^2-4
y=±√(x+4)/7
400
Given function –3x^3-x^2+4, what would be the new equation after it is reflected over the y-axis?
3x^3–x^2+4
500
For the Quadratic Function F(x)= -x^2 + 4x + 12 with the domain [0,5], find the range
[7,12]
500
What would the new equation be if you dilate y=x^2 by 7 horizontally, 3 vertically, and moved -15 units.
y= 3(x/7)^2–15
500
If F(x)= x^2 within the domain 0≤x≤5, and G(x)= 2x - 3 within the domain -2≤x≤0, then what is the domain and range of F(G(x))?
Domain:3/2≤x≤0 Range: 0≤y≤9
500
Give the equation of the inverse of function y=13x^2–7
y=±√(x+7)/13
500
What does the transformation of f(x) to |f(x)| do?
1. Reflects all negative values of f over the x-axis. 2. Leaves all other positive values alone.
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