Question 1

Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$. $y = \sqrt { - x + 4 }$

Accepted Answer

A)  First a vertical shift of 4 units up then a reflection in the $y$-axis. 
B)  First a horizontal shift of 4 units to the left then a reflection in the $y$-axis. 
C)  First a vertical shift of 4 units up then a reflection in the $x$-axis. 
D)  First a horizontal shift of 4 units to the left, then a vertical shift of 4 units up and then a reflection in the $y$-axis. 
E)  First a horizontal shift of 4 units to the left then a reflection in the $x$-axis. 
A)  First a vertical shift of 4 units up then a reflection in the $y$-axis. 
B)  First a horizontal shift of 4 units to the left then a reflection in the $y$-axis. 
C)  First a vertical shift of 4 units up then a reflection in the $x$-axis. 
D)  First a horizontal shift of 4 units to the left, then a vertical shift of 4 units up and then a reflection in the $y$-axis. 
E)  First a horizontal shift of 4 units to the left then a reflection in the $x$-axis.

Question 2

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$y = \left| \frac { 4 } { 9 } x \right|$

Accepted Answer

A)  vertical shift of $\frac { 4 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 4 }$ units 
C)  vertical shrink of $\frac { 4 } { 9 }$ units 
D)  horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units 
E)  horizontal shrink of $\frac { 4 } { 9 }$ units 
A)  vertical shift of $\frac { 4 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 4 }$ units 
C)  vertical shrink of $\frac { 4 } { 9 }$ units 
D)  horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units 
E)  horizontal shrink of $\frac { 4 } { 9 }$ units

Question 3

Find $f \circ g$.
$f ( x ) = 3 x - 2$
$g ( x ) = x - 5$

Accepted Answer

A)  $( f \circ g ) ( x ) = 3 x - 17$ 
B)  $( f \circ g ) ( x ) = 3 x - 7$ 
C)  $( f \circ g ) ( x ) = 3 x ^ { 2 } - 17 x + 10$ 
D)  $( f \circ g ) ( x ) = 2 x + 3$ 
E)  $( f \circ g ) ( x ) = 2 x - 7$ 
A)  $( f \circ g ) ( x ) = 3 x - 17$ 
B)  $( f \circ g ) ( x ) = 3 x - 7$ 
C)  $( f \circ g ) ( x ) = 3 x ^ { 2 } - 17 x + 10$ 
D)  $( f \circ g ) ( x ) = 2 x + 3$ 
E)  $( f \circ g ) ( x ) = 2 x - 7$

Question 4

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$. $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Accepted Answer

A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C)  $g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $\quad g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$ 
A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C)  $g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $\quad g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Question 5

Evaluate the function at the specified value of the independent variable and simplify.
$\begin{array} { l } 
q ( p ) = \frac { - 2 p } { 5 p - 2 } \
q ( x - 9 )
\end{array}$

Accepted Answer

A)  $\frac { - 2 x + 18 } { 5 x - 47 }$ 
B)  $\frac { - 2 x - 18 } { 5 x - 47 }$ 
C)  $\frac { - 2 p + 18 } { 5 p - 47 }$ 
D)  $\frac { 18 } { 43 }$ 
E)  $- \frac { 18 } { 47 }$ 
A)  $\frac { - 2 x + 18 } { 5 x - 47 }$ 
B)  $\frac { - 2 x - 18 } { 5 x - 47 }$ 
C)  $\frac { - 2 p + 18 } { 5 p - 47 }$ 
D)  $\frac { 18 } { 43 }$ 
E)  $- \frac { 18 } { 47 }$

Question 6

Find $f \circ g$.
$f ( x ) = x + 4 \quad g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$

Accepted Answer

A)  $( f \circ g ) ( x ) = \frac { 3 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 3 } { x ^ { 2 } + 8 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 4 x ^ { 2 } - 1 } { x ^ { 2 } - 16 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 16 }$ 
E)  $( f \circ g ) ( x ) = \frac { 4 x ^ { 2 } - 61 } { x ^ { 2 } - 16 }$ 
A)  $( f \circ g ) ( x ) = \frac { 3 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 3 } { x ^ { 2 } + 8 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 4 x ^ { 2 } - 1 } { x ^ { 2 } - 16 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 16 }$ 
E)  $( f \circ g ) ( x ) = \frac { 4 x ^ { 2 } - 61 } { x ^ { 2 } - 16 }$

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)  $\quad f ( x ) = - | x - 1 | + 1$ 
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)  $\quad f ( x ) = - | x - 1 | + 1$

Question 8

Determine a piecewise-defined function for the graph shown below.

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \ - ( x - 1 ) ^ { 2 } + 1 , & x > 1 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 0 \ - ( x - 1 ) ^ { 2 } + 1 , & x \leq 0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 1 \ - x ^ { 2 } , & x \leq 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 0 \ - x ^ { 2 } , & x \leq 1 \end{array} \right.$ 
E)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \ - ( x - 1 ) ^ { 2 } , & x > 1 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \ - ( x - 1 ) ^ { 2 } + 1 , & x > 1 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 0 \ - ( x - 1 ) ^ { 2 } + 1 , & x \leq 0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 1 \ - x ^ { 2 } , & x \leq 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 0 \ - x ^ { 2 } , & x \leq 1 \end{array} \right.$ 
E)  $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \ - ( x - 1 ) ^ { 2 } , & x > 1 \end{array} \right.$

Question 9

Find the difference quotient and simplify your answer.
$f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Accepted Answer

A)  $6 + h$ 
B)  $- 18 - 2 s - \frac { 16 } { s }$ 
C)  $- 2 - 2 s - \frac { 16 } { s }$ 
D)  $- 2 - 2 h$ 
E)  $- 18 - 2 h$ 
A)  $6 + h$ 
B)  $- 18 - 2 s - \frac { 16 } { s }$ 
C)  $- 2 - 2 s - \frac { 16 } { s }$ 
D)  $- 2 - 2 h$ 
E)  $- 18 - 2 h$

Question 10

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$.
$( f g ) ( - 1 )$

Accepted Answer

A)  $- 32$ 
B)  $- 48$ 
C)  $- 46$ 
D)  40 
E)  $- 50$ 
A)  $- 32$ 
B)  $- 48$ 
C)  $- 46$ 
D)  40 
E)  $- 50$

Question 11

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 12

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$.
$y = [ 5 ( x - 2 ) ] ^ { 3 }$

Accepted Answer

A)  vertical shift of 2 units down 
B)  vertical shift of 2 units down horizontal shrink of $\frac { 1 } { 5 }$ units 
C)  horizontal shift of 2 units to the right horizontal shrink of $\frac { 1 } { 125 }$ units 
D)  horizontal shift of 2 units to the right horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 2 units to the right vertical shift of 5 units down 
A)  vertical shift of 2 units down 
B)  vertical shift of 2 units down horizontal shrink of $\frac { 1 } { 5 }$ units 
C)  horizontal shift of 2 units to the right horizontal shrink of $\frac { 1 } { 125 }$ units 
D)  horizontal shift of 2 units to the right horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 2 units to the right vertical shift of 5 units down

Question 13

Find the domain of the function.
$f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Accepted Answer

A)  $- 3 \leq y \leq 3$ 
B)  $y \leq - 3$ or $y \geq 3$ 
C)  $y \geq 0$ 
D)  $y \leq 3$ 
E)  all real numbers 
A)  $- 3 \leq y \leq 3$ 
B)  $y \leq - 3$ or $y \geq 3$ 
C)  $y \geq 0$ 
D)  $y \leq 3$ 
E)  all real numbers

Question 14

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

Accepted Answer

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

Question 15

Find $g \circ f$.
$f ( x ) = x + 2$
$g ( x ) = x ^ { 2 }$

Accepted Answer

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

Question 16

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$f ( x ) = - x ^ { 3 } + 3 x + 1$

Accepted Answer

A)  increasing on $( - \infty , - 1 )$
decreasing on $( - 1,1 )$
increasing on $( 1 , \infty )$ 
B)  decreasing on $( - \infty , 0 )$
increasing on $( 0 , \infty )$ 
C)  decreasing on $( - \infty , \infty )$ 
D)  increasing on $( - \infty , \infty )$ 
E)  decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$ 
A)  increasing on $( - \infty , - 1 )$
decreasing on $( - 1,1 )$
increasing on $( 1 , \infty )$ 
B)  decreasing on $( - \infty , 0 )$
increasing on $( 0 , \infty )$ 
C)  decreasing on $( - \infty , \infty )$ 
D)  increasing on $( - \infty , \infty )$ 
E)  decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$

Question 17

Use the graph of $f ( x ) = x ^ { 2 }$
to write an equation for the function whose graph is shown.

Accepted Answer

A)  $f ( x ) = ( x + 1 ) ^ { 2 } - 2$ 
B)  $f ( x ) = ( x - 1 ) ^ { 2 } - 2$ 
C)  $f ( x ) = ( x + 1 ) ^ { 2 } + 2$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } - 2$ 
E)  $f ( x ) = \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 2$ 
A)  $f ( x ) = ( x + 1 ) ^ { 2 } - 2$ 
B)  $f ( x ) = ( x - 1 ) ^ { 2 } - 2$ 
C)  $f ( x ) = ( x + 1 ) ^ { 2 } + 2$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } - 2$ 
E)  $f ( x ) = \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 2$

Question 18

Show algebraically that the functions $f$ and $g$ shown below are inverse functions.
$f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \quad g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Accepted Answer

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

Question 19

Find the slope-intercept form of the line passing through the points.
$( - 1 , - 6 ) , ( 0 , - 2 )$

Accepted Answer

A)  $y = 4 x + 23$ 
B)  $y = 4 x - 2$ 
C)  $y = \frac { 1 } { 4 } x - \frac { 23 } { 4 }$ 
D)  $y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }$ 
E)  $y = - 4 x - 10$ 
A)  $y = 4 x + 23$ 
B)  $y = 4 x - 2$ 
C)  $y = \frac { 1 } { 4 } x - \frac { 23 } { 4 }$ 
D)  $y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }$ 
E)  $y = - 4 x - 10$

Question 20

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$.

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$ 
C)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 10 } { 3 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$ 
C)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 10 } { 3 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , \infty )$

Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$ . $y = \sqrt { - x + 4 }$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$

Find $f \circ g$ . $f ( x ) = 3 x - 2$ $g ( x ) = x - 5$

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Evaluate the function at the specified value of the independent variable and simplify. q(p)= q(x-9)

Find $f \circ g$ . $f ( x ) = x + 4 \quad g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$

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

Determine a piecewise-defined function for the graph shown below.

Find the difference quotient and simplify your answer. $f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$ . $( f g ) ( - 1 )$

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

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x - 2 ) ] ^ { 3 }$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

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

Find $g \circ f$ . $f ( x ) = x + 2$ $g ( x ) = x ^ { 2 }$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = - x ^ { 3 } + 3 x + 1$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \quad g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$ .

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

Compare the graph of the following function with the graph of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ . y=−x+4y = \sqrt { - x + 4 }y=−x+4​

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣49x∣y = \left| \frac { 4 } { 9 } x \right|y=​94​x​

Find f∘gf \circ gf∘g . f(x)=3x−2f ( x ) = 3 x - 2f(x)=3x−2 g(x)=x−5g ( x ) = x - 5g(x)=x−5

Use function notation to write ggg in terms of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ . g(x)=−13x−8+7g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7g(x)=−31​x−8​+7

Evaluate the function at the specified value of the independent variable and simplify. q(p)= q(x-9)

Find f∘gf \circ gf∘g . f(x)=x+4g(x)=3x2−16f ( x ) = x + 4 \quad g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }f(x)=x+4g(x)=x2−163​

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

Determine a piecewise-defined function for the graph shown below.

Find the difference quotient and simplify your answer. f(s)=−2s2−2s,f(4+h)−f(4)h,h≠0f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0f(s)=−2s2−2s,hf(4+h)−f(4)​,h=0

Evaluate the indicated function for f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5 and g(x)=x+9g ( x ) = x + 9g(x)=x+9 . (fg)(−1)( f g ) ( - 1 )(fg)(−1)

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) .

Compare the graph of the following function with the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . y=[5(x−2)]3y = [ 5 ( x - 2 ) ] ^ { 3 }y=[5(x−2)]3

Find the domain of the function. f(y)=9−y2f ( y ) = \sqrt { 9 - y ^ { 2 } }f(y)=9−y2​

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

Find g∘fg \circ fg∘f . f(x)=x+2f ( x ) = x + 2f(x)=x+2 g(x)=x2g ( x ) = x ^ { 2 }g(x)=x2

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. f(x)=−x3+3x+1f ( x ) = - x ^ { 3 } + 3 x + 1f(x)=−x3+3x+1

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write an equation for the function whose graph is shown.

Show algebraically that the functions fff and ggg shown below are inverse functions. f(x)=8x−73,g(x)=x3+78f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \quad g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }f(x)=38x−7​,g(x)=8x3+7​

Find the slope-intercept form of the line passing through the points. (−1,−6),(0,−2)( - 1 , - 6 ) , ( 0 , - 2 )(−1,−6),(0,−2)

Given f(x)=10x2−9f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }f(x)=x2−910​ and g(x)=x+3g ( x ) = x + 3g(x)=x+3 determine the domain of f∘gf \circ gf∘g .

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 $f ( x ) = \sqrt { x }$ . $y = \sqrt { - x + 4 }$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$

Find $f \circ g$ . $f ( x ) = 3 x - 2$ $g ( x ) = x - 5$

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Find $f \circ g$ . $f ( x ) = x + 4 \quad g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$

Find the difference quotient and simplify your answer. $f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$ . $( f g ) ( - 1 )$

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

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x - 2 ) ] ^ { 3 }$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Find $g \circ f$ . $f ( x ) = x + 2$ $g ( x ) = x ^ { 2 }$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = - x ^ { 3 } + 3 x + 1$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \quad g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$ .