Module 1 Review

Module 1 Review

Analyzing Functions

Characteristics of Functions

Transformations of Functions

Inverses of Functions

Function Characteristics

Multiple Choice

• $\left(-3,5\right]$

• $\left[-3,5\right)$

• $\left(-3,5\right)$

• $\left[-3,5\right]$

Multiple Choice

Select the interval notation that represent the inequality shown:  $-23\le x<9$  

•  $\left(-23,9\right)$  

•  $\left(-23,9\right]$  

•  $\left[-23,9\right)$  

•  $\left[9,-23\right)$  

Multiple Select

Select all the intervals where the function is increasing.

• $0\le t\le105$

• $105\le t\le825$

• $825\le t\le1600$

Multiple Choice

The graph has a maximum of ?????? , at  $t=$  ?????

•  $1541$ at $t=105$ 

•  $105$  at  $t=1541$  
  

•  $825$ at  $t=1487$  

•  $1487$  at  $t=825$  

Multiple Choice

The graph has a minimum of ?????? , at  $t=$  ?????

•  $1541$ at $t=105$ 

•  $105$  at  $t=1541$  
  

•  $825$ at  $t=1487$  

•  $1487$  at  $t=825$  

Transformations

Fill in the Blanks

Write a function for a transformation of f(x) translated 5 units left.

g(x)=

Fill in the Blanks

Write a function for a transformation of f(x) translated 6 units right.

g(x)=

Fill in the Blanks

Write a function for a transformation of f(x) translated 2 units down.

g(x)=

Fill in the Blanks

Write a function for a transformation of f(x) with a vertical stretch by a factor of 3

g(x)=

Multiple Choice

Write a function for a transformation of f(x) with a horizontal stretch by a factor of 4

g(x)=

• $f\left(4x\right)$

• $4f\left(x\right)$

• $f\left(\frac{1}{4}x\right)$

• $\frac{1}{4}f\left(x\right)$

Multiple Select

Compared to the function  $f\left(x\right)$  , what type of transformation is the function  $-f\left(x\right)$ and how will it look? 

• reflect over x-axis

• reflect over y-axis

• flips upside down

• flips left-to-right

Multiple Select

Compared to the function  $f\left(x\right)$  , what type of transformation is the function  $f\left(-x\right)$ and how will it look? 

• reflect over x-axis

• reflect over y-axis

• flips upside down

• flips left-to-right

Domain, Range, End Behavior

Multiple Choice

Find the domain of the function shown.

 $g\left(x\right)=x^2-4$  

•  $-4\le x<\infty$  

•  $-\infty<x<\infty$  

•  $+\infty<x<+\infty$  

•  $\infty<y<-4$  

Multiple Choice

Find the range of the function shown.

 $g\left(x\right)=x^2-4$  

•  $-4\le y<\infty$  

•  $-\infty<y<\infty$  

•  $+\infty<y<+\infty$  

•  $\infty<y<-4$  

Multiple Choice

Find the end behavior of the function shown.

 $g\left(x\right)=x^2-4$  

•  $x\rightarrow+\infty,\ g\left(x\right)\rightarrow+\infty$  

   $x\rightarrow-\infty,\ g\left(x\right)\rightarrow-\infty$  
  

•  $x\rightarrow+\infty,\ g\left(x\right)\rightarrow-\infty$  

   $x\rightarrow-\infty,\ g\left(x\right)\rightarrow-\infty$  
  

•  $x\rightarrow+\infty,\ g\left(x\right)\rightarrow+\infty$ 
   $x\rightarrow-\infty,\ g\left(x\right)\rightarrow+\infty$   

Inverses of Functions

Fill in the Blanks

Find the inverse of the function:

 $f(x)=\frac{x+5}{6}$  

 $f^{-1}\left(x\right)=$     ?

Multiple Choice

Find the inverse of the function: $g\left(x\right)=2x-15$  

•  $g^{-1}\left(x\right)=\frac{x+15}{2}$  

•  $g^{-1}\left(x\right)=\frac{1}{2}x+15$  

•  $g^{-1}\left(x\right)=\frac{15}{2x}$  

•  $g^{-1}\left(x\right)=\frac{x-2}{15}$  

Multiple Choice

Given the table of values, which of the following ordered pairs are found on the graph of the inverse function?

Fill in the Blanks

Find the inverse of the function:

 $f(x)=\frac{1}{2}x-6$  

 $f^{-1}\left(x\right)=$     ?