Question 1

Decide whether the two functions shown in the graph below appear to be inverse functions of each other.

Accepted Answer

A)  yes 
B)  no 
C)  not enough information 
A)  yes 
B)  no 
C)  not enough information

Question 2

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$y = \left| \frac { 3 } { 4 } x \right|$

Accepted Answer

A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units 
D)  horizontal shrink of $\frac { 3 } { 4 }$ units vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units 
A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units 
D)  horizontal shrink of $\frac { 3 } { 4 }$ units vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units

Question 3

Determine algebraically whether the following function is one-to-one.
$f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$, where $x > 0$

Accepted Answer

A) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { not one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
\pm a & = \quad \pm b
\end{aligned}$ 
B) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 } { 3 + 6 } & = \frac { 5 } { 3 + 6 } ; \text { one-to-one } \
\frac { 5 } { 6 } & = \frac { 3 } { 6 } \
a & = b
\end{aligned}$ 
C) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } ; \text { one-to-one } \
\frac { 5 } { 3 } & = \frac { 5 } { 3 } \
a & = b
\end{aligned}$ 
D) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 9 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 9 b ^ { 2 } } \
\frac { 5 a } { 9 } & = \frac { 5 b } { 9 } \
5 a & = 5 b\text { one-to-one } \
a & =  b
\end{aligned}$ 
E)  $\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 }$
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
a & = b
\end{aligned}$ 
A) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { not one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
\pm a & = \quad \pm b
\end{aligned}$ 
B) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 } { 3 + 6 } & = \frac { 5 } { 3 + 6 } ; \text { one-to-one } \
\frac { 5 } { 6 } & = \frac { 3 } { 6 } \
a & = b
\end{aligned}$ 
C) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } ; \text { one-to-one } \
\frac { 5 } { 3 } & = \frac { 5 } { 3 } \
a & = b
\end{aligned}$ 
D) 
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 9 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 9 b ^ { 2 } } \
\frac { 5 a } { 9 } & = \frac { 5 b } { 9 } \
5 a & = 5 b\text { one-to-one } \
a & =  b
\end{aligned}$ 
E)  $\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 }$
$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
a & = b
\end{aligned}$

Question 4

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$.

Accepted Answer

A)  $( g \circ f ) ^ { - 1 } = \frac { 5 x + 11 } { 4 }$ 
B)  $( g \circ f ) ^ { - 1 } = 5 x - 42$ 
C)  $( g \circ f ) ^ { - 1 } = \frac { x - 13 } { 5 }$ 
D)  $( g \circ f ) ^ { - 1 } = \frac { - 7 x - 7 } { 5 }$ 
E)  $( g \circ f ) ^ { - 1 } = 5 x + 13$ 
A)  $( g \circ f ) ^ { - 1 } = \frac { 5 x + 11 } { 4 }$ 
B)  $( g \circ f ) ^ { - 1 } = 5 x - 42$ 
C)  $( g \circ f ) ^ { - 1 } = \frac { x - 13 } { 5 }$ 
D)  $( g \circ f ) ^ { - 1 } = \frac { - 7 x - 7 } { 5 }$ 
E)  $( g \circ f ) ^ { - 1 } = 5 x + 13$

Question 5

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Accepted Answer

A)  slope: 0 
B)  slope: 1 
C)  slope: $- 5$ 
D)  slope: $- \frac { 1 } { 5 }$ 
E)  slope: undefined 
A)  slope: 0 
B)  slope: 1 
C)  slope: $- 5$ 
D)  slope: $- \frac { 1 } { 5 }$ 
E)  slope: undefined

Question 6

Find all real values of $x$ such that $f ( x ) = 0$.
$f ( x ) = \frac { - 2 x + 5 } { 5 }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\pm \frac { 1 } { 2 }$ 
C)  $\pm \frac { 5 } { 2 }$ 
D)  $\frac { 5 } { 2 }$ 
E)  $- \frac { 5 } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\pm \frac { 1 } { 2 }$ 
C)  $\pm \frac { 5 } { 2 }$ 
D)  $\frac { 5 } { 2 }$ 
E)  $- \frac { 5 } { 2 }$

Question 7

Determine an equation that may represented by the graph shown below.

Accepted Answer

A)  $f ( x ) = | x - 1 | - 1$ 
B)  $f ( x ) = - | x - 1 | + 1$ 
C)  $f ( x ) = | x - 1 | + 1$ 
D)  $f ( x ) = | x + 1 | + 1$ 
E)  $f ( x ) = | x + 1 | - 1$ 
A)  $f ( x ) = | x - 1 | - 1$ 
B)  $f ( x ) = - | x - 1 | + 1$ 
C)  $f ( x ) = | x - 1 | + 1$ 
D)  $f ( x ) = | x + 1 | + 1$ 
E)  $f ( x ) = | x + 1 | - 1$

Question 8

Find $( f g ) ( x )$.
$$f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$$

Accepted Answer

A)  $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$ 
B)  $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$ 
C)  $( f g ) ( x ) = \sqrt { - 13 x + 6 }$ 
D)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$ 
E)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$ 
A)  $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$ 
B)  $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$ 
C)  $( f g ) ( x ) = \sqrt { - 13 x + 6 }$ 
D)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$ 
E)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$

Question 9

Find $f \circ g$.
$f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

Accepted Answer

A)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } + 4 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } + 3 } { x ^ { 2 } - 4 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 4 }$ 
E)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } - 3 } { x ^ { 2 } - 4 }$ 
A)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } + 4 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } + 3 } { x ^ { 2 } - 4 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 4 }$ 
E)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } - 3 } { x ^ { 2 } - 4 }$

Question 10

Use the graphs of $f$ and $g$, shown below, to graph $h ( x ) = ( f + g ) ( x )$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 11

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$.
$f ( x ) = - | x + 7 | - 1$, where $x > - 7$

Accepted Answer

A)  Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$ 
B)  Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$ 
C)  Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$ 
D)  Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$ 
B)  Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$ 
C)  Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$ 
D)  Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question 12

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

Accepted Answer

A)  $y = 3 x + 2$ 
B)  $y = 3 x + 10$ 
C)  $y = \frac { 1 } { 3 } x - \frac { 2 } { 3 }$ 
D)  $y = - \frac { 1 } { 3 } x - \frac { 10 } { 3 }$ 
E)  $y = - 3 x - 14$ 
A)  $y = 3 x + 2$ 
B)  $y = 3 x + 10$ 
C)  $y = \frac { 1 } { 3 } x - \frac { 2 } { 3 }$ 
D)  $y = - \frac { 1 } { 3 } x - \frac { 10 } { 3 }$ 
E)  $y = - 3 x - 14$

Question 13

Find the domain of the function.
$g ( w ) = \frac { 4 w } { w + 9 }$

Accepted Answer

A)  all real numbers $w \neq - 9$ 
B)  all real numbers $w \neq - 9 , w \neq 0$ 
C)  all real numbers 
D)  $w = - 9 , w = 0$ 
E)  $w = - 9$ 
A)  all real numbers $w \neq - 9$ 
B)  all real numbers $w \neq - 9 , w \neq 0$ 
C)  all real numbers 
D)  $w = - 9 , w = 0$ 
E)  $w = - 9$

Question 14

Use the graphs of $f$ and $g$ to evaluate the function.
$( f \circ g ) ( 1 )$

Accepted Answer

A)  9 
B)  $- 1$ 
C)  0 
D)  $- 4$ 
E)  $- 2$ 
A)  9 
B)  $- 1$ 
C)  0 
D)  $- 4$ 
E)  $- 2$

Question 15

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$.
$y = [ 5 ( x + 10 ) ] ^ { 3 }$

Accepted Answer

A)  vertical shift of 10 units up 
B)  vertical shift of 10 units up horizontal shrink of $\frac { 1 } { 5 }$ units 
C)  horizontal shift of 10 units to the left horizontal shrink of $\frac { 1 } { 125 }$ units 
D)  horizontal shift of 10 units to the left horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 10 units to the left vertical shift of 5 units up 
A)  vertical shift of 10 units up 
B)  vertical shift of 10 units up horizontal shrink of $\frac { 1 } { 5 }$ units 
C)  horizontal shift of 10 units to the left horizontal shrink of $\frac { 1 } { 125 }$ units 
D)  horizontal shift of 10 units to the left horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 10 units to the left vertical shift of 5 units up

Question 16

Evaluate the following function at the specified value of the independent variable and simplify.
$$f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$$

Accepted Answer

A)  20 
B)  0 
C)  $- 7$ 
D)  13 
E)  undefined 
A)  20 
B)  0 
C)  $- 7$ 
D)  13 
E)  undefined

Question 17

Find all real values of $x$ such that $f ( x ) = 0$. $f ( x ) = 49 x ^ { 2 } - 64$

Accepted Answer

A)  $\pm \frac { 7 } { 8 }$ 
B)  $\pm \frac { 8 } { 7 }$ 
C)  $\pm \frac { 64 } { 49 }$ 
D)  $- \frac { 64 } { 49 }$ 
E)  $\frac { 8 } { 7 }$ 
A)  $\pm \frac { 7 } { 8 }$ 
B)  $\pm \frac { 8 } { 7 }$ 
C)  $\pm \frac { 64 } { 49 }$ 
D)  $- \frac { 64 } { 49 }$ 
E)  $\frac { 8 } { 7 }$

Question 18

Use the graph of $f$ to sketch the graph of the function indicated below.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 19

Find the inverse function of $f$.
$f ( x ) = x ^ { 5 } + 5$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 5$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 5$ 
A)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 5$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 5$

Question 20

The average lengths $L$ of cellular phone calls in minutes from 1999 to 2004 are shown in the table below.

Use the regression feature of a graphing utility to find a linear model for the data. Let $t$ represent the year, with $t = 9$ corresponding to 1999 . Use the model to predict the average lengths of cellular phone calls for the year 2015 . Round your answer to two decimal places.

Accepted Answer

A)  $4.37$ minutes 
B)  $8.74$ minutes 
C)  $5.37$ minutes 
D)  $3.37$ minutes 
E)  $2.19$ minutes 
A)  $4.37$ minutes 
B)  $8.74$ minutes 
C)  $5.37$ minutes 
D)  $3.37$ minutes 
E)  $2.19$ minutes

Decide whether the two functions shown in the graph below appear to be inverse functions of each other.

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

Determine algebraically whether the following function is one-to-one. $f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$ , where $x > 0$

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$ .

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 2 x + 5 } { 5 }$

Determine an equation that may represented by the graph shown below.

Find $( f g ) ( x )$ . $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Find $f \circ g$ . $f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ . $f ( x ) = - | x + 7 | - 1$ , where $x > - 7$

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

Find the domain of the function. $g ( w ) = \frac { 4 w } { w + 9 }$

Use the graphs of $f$ and $g$ to evaluate the function. $( f \circ g ) ( 1 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 1 )$

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x + 10 ) ] ^ { 3 }$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Use the graph of $f$ to sketch the graph of the function indicated below.

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } + 5$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

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Exam 1: Functions and Their Graphs

Decide whether the two functions shown in the graph below appear to be inverse functions of each other.

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣34x∣y = \left| \frac { 3 } { 4 } x \right|y=​43​x​

Determine algebraically whether the following function is one-to-one. f(x)=5x23x2+6f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }f(x)=3x2+65x2​ , where x>0x > 0x>0

Use the functions f(x)=x+4f ( x ) = x + 4f(x)=x+4 and g(x)=5x−7g ( x ) = 5 x - 7g(x)=5x−7 to find (g∘f)−1( g \circ f ) ^ { - 1 }(g∘f)−1 .

Plot the points and find the slope of the line passing through the pair of points. (3,4),(−2,4)( 3,4 ) , ( - 2,4 )(3,4),(−2,4)

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=−2x+55f ( x ) = \frac { - 2 x + 5 } { 5 }f(x)=5−2x+5​

Determine an equation that may represented by the graph shown below.

Find (fg)(x)( f g ) ( x )(fg)(x) . f(x)=−5xg(x)=−8x+6f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }f(x)=−5x​g(x)=−8x+6​

Find f∘gf \circ gf∘g . f(x)=x+2g(x)=5x2−4f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }f(x)=x+2g(x)=x2−45​

Use the graphs of fff and ggg , shown below, to graph h(x)=(f+g)(x)h ( x ) = ( f + g ) ( x )h(x)=(f+g)(x) .

Determine the domain and range of the inverse function f−1f ^ { - 1 }f−1 of the following function fff . f(x)=−∣x+7∣−1f ( x ) = - | x + 7 | - 1f(x)=−∣x+7∣−1 , where x>−7x > - 7x>−7

Find the slope-intercept form of the line passing through the points. (−4,−2),(−1,7)( - 4 , - 2 ) , ( - 1,7 )(−4,−2),(−1,7)

Find the domain of the function. g(w)=4ww+9g ( w ) = \frac { 4 w } { w + 9 }g(w)=w+94w​

Use the graphs of fff and ggg to evaluate the function. (f∘g)(1)( f \circ g ) ( 1 )(f∘g)(1)

Compare the graph of the following function with the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . y=[5(x+10)]3y = [ 5 ( x + 10 ) ] ^ { 3 }y=[5(x+10)]3

Evaluate the following function at the specified value of the independent variable and simplify. f(w)=−7w2+20w2;f(0)f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )f(w)=w2−7w2+20​;f(0)

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=49x2−64f ( x ) = 49 x ^ { 2 } - 64f(x)=49x2−64

Use the graph of fff to sketch the graph of the function indicated below.

Find the inverse function of fff . f(x)=x5+5f ( x ) = x ^ { 5 } + 5f(x)=x5+5

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

Determine algebraically whether the following function is one-to-one. $f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$ , where $x > 0$

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$ .

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 2 x + 5 } { 5 }$

Find $( f g ) ( x )$ . $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Find $f \circ g$ . $f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ . $f ( x ) = - | x + 7 | - 1$ , where $x > - 7$

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

Find the domain of the function. $g ( w ) = \frac { 4 w } { w + 9 }$

Use the graphs of $f$ and $g$ to evaluate the function. $( f \circ g ) ( 1 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 1 )$

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x + 10 ) ] ^ { 3 }$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Use the graph of $f$ to sketch the graph of the function indicated below.

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } + 5$