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

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

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?