Analyzing Functions Test Review

Describe the transformations from

 $f\left(x\right)=x^2\ to\ f\left(x\right)=-\left(x-3\right)^2+4$  

• Vertical Reflection over X axis
  

• Horizontal Reflection over Y axis

• Right 3

• Left 3

• Up 4
  

Describe the transformations from

 $f\left(x\right)=x^2\ to\ f\left(x\right)=2\left(x+1\right)^2-1$  

• Vertical Stretch by 2
  

• Vertical Compression by 1/2

• Right 1

• Left 1

• Down 1
  

Describe the domain of the graph pictured

•  $0\le x\le4$  

•  $-4\le x\le4$  

•  $4\le x\le-4$  

•  $-4\le y\le4$  

Describe the range of the graph pictured

•  $0\le x\le4$  

•  $0\le y\le0$  

•  $-4\le y\le4$  

•  $0\le y\le4$  

If the parent function f(x) = $x^2$  is translated using the following description, what is the resulting function?

Vertical Compression by 1/2 then shift left 2 and up 6

•  $g\left(x\right)=2\left(x+2\right)^2+6$  

•  $g\left(x\right)=\frac{1}{2}\left(x-2\right)^2+6$  

•  $g\left(x\right)=\frac{1}{2}\left(x-2\right)^2-6$  

•  $g\left(x\right)=\frac{1}{2}\left(x+2\right)^2+6$  

Over which interval(s) is the graph increasing?

•  $-2\le x\le0$  

•  $0\le x\le2$  

•  $-2\le x\le\infty$  

•  $-3<x\le1$  

Over which intervals is the average rate of change negative for the table shown?

• A

• B

• C

• D

Which statement best describes the domain?

• (-8,8)

• [-8,8)

• [-8,8]

• (-8,8]

Which statement best describes the domain?

• $-4\le y\le6$

• $-4<y<6$
  

• $-4\le y<6$

• $-4<y\le6$
  

Find the inverse of f(x) = 6x - 13

•  $f^{-1}\left(x\right)=\frac{x+13}{-6}$  

•  $f^{-1}\left(x\right)=-6x+13$  

•  $f^{-1}\left(x\right)=\frac{x+13}{6}$  

•  $f^{-1}\left(x\right)=\frac{x-6}{13}$