Question 1

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function.
$f ( x ) = - | x - 4 | + 2$

Accepted Answer

A)  $[ - 4 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ - 2,4 ]$ 
E)  $( - \infty , 2 ]$ 
A)  $[ - 4 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ - 2,4 ]$ 
E)  $( - \infty , 2 ]$

Question 2

Does the table describe a function?
$\begin{array}{|c|c|c|c|c|c|}
\hline \text { Input value } & -6 & -3 & 0 & 3 & 6 \
\hline \text { Output value } & 11 & 11 & 11 & 11 & 11 \
\hline
\end{array}$

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 3

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

Accepted Answer

A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation 
A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation

Question 4

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Accepted Answer

A)  even 
B)  odd 
C)  cannot be determined 
D)  neither 
A)  even 
B)  odd 
C)  cannot be determined 
D)  neither

Question 5

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$$

Accepted Answer

A)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$ 
B)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$ 
C)  $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$ 
D)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$ 
E)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$ 
A)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$ 
B)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$ 
C)  $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$ 
D)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$ 
E)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$

Question 6

Given the following function, $h ( x )$, find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$.
$h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Accepted Answer

A)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$ 
B)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$ 
D)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$ 
E)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , \quad g ( x ) = x + 11$ 
A)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$ 
B)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$ 
D)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$ 
E)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , \quad g ( x ) = x + 11$

Question 7

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$

Accepted Answer

A)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 2 }$ 
D)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x + 9 ) ]$ 
A)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 2 }$ 
D)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x + 9 ) ]$

Question 8

Find all real values of $x$ such that $f ( x ) = 0$.
$f ( x ) = \frac { - 3 x - 2 } { 5 }$

Accepted Answer

A)  $- \frac { 2 } { 15 }$ 
B)  $\pm \frac { 2 } { 15 }$ 
C)  $\pm \frac { 2 } { 3 }$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $\frac { 2 } { 3 }$ 
A)  $- \frac { 2 } { 15 }$ 
B)  $\pm \frac { 2 } { 15 }$ 
C)  $\pm \frac { 2 } { 3 }$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $\frac { 2 } { 3 }$

Question 9

Find the value(s) of $x$ for which $f ( x ) = g ( x )$.
$f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Accepted Answer

A)  $5,18 , \frac { 2 } { 9 }$ 
B)  $5 , - 13 , \frac { 2 } { 9 }$ 
C)  3,1 
D)  $- 3 , - 1$ 
E)  $8 , \frac { 2 } { 9 }$ 
A)  $5,18 , \frac { 2 } { 9 }$ 
B)  $5 , - 13 , \frac { 2 } { 9 }$ 
C)  3,1 
D)  $- 3 , - 1$ 
E)  $8 , \frac { 2 } { 9 }$

Question 10

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$.

Accepted Answer

A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$

Question 11

Find the domain of the function.
$f ( t ) = \sqrt { 64 - t ^ { 2 } }$

Accepted Answer

A)  $- 8 \leq t \leq 8$ 
B)  $t \leq - 8$ or $t \geq 8$ 
C)  $t \geq 0$ 
D)  $t \leq 8$ 
E)  all real numbers 
A)  $- 8 \leq t \leq 8$ 
B)  $t \leq - 8$ or $t \geq 8$ 
C)  $t \geq 0$ 
D)  $t \leq 8$ 
E)  all real numbers

Question 12

Find the value(s) of $x$ for which $f ( x ) = g ( x )$.
$f ( x ) = x ^ { 2 } - 11 x - 36$
$g ( x ) = - 7 x - 4$

Accepted Answer

A)  $- 36 , - 25 , - \frac { 4 } { 7 }$ 
B)  $- 36 , - 11 , - \frac { 4 } { 7 }$ 
C)  $8 , - 4$ 
D)  $- 8,4$ 
E)  $47 , - \frac { 4 } { 7 }$ 
A)  $- 36 , - 25 , - \frac { 4 } { 7 }$ 
B)  $- 36 , - 11 , - \frac { 4 } { 7 }$ 
C)  $8 , - 4$ 
D)  $- 8,4$ 
E)  $47 , - \frac { 4 } { 7 }$

Question 13

Find the inverse function of $f$.
$f ( x ) = x ^ { 5 } - 1$

Accepted Answer

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

Question 14

Which equation does not represent $y$ as a function of $x$ ?

Accepted Answer

A)  $x = 2 y + 5$ 
B)  $\quad x = 6$ 
C)  $y = - 5 x - 7$ 
D)  $y = \left| 6 + 9 x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 8 + 4 x }$ 
A)  $x = 2 y + 5$ 
B)  $\quad x = 6$ 
C)  $y = - 5 x - 7$ 
D)  $y = \left| 6 + 9 x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 8 + 4 x }$

Question 15

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$.
$f ( x ) = - x ^ { 2 } + 4 x$

Accepted Answer

A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$ 
A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$

Question 16

Use the graph of the function to find the domain and range of $f$.

Accepted Answer

A)  domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B)  domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $\{ - 2 , - 1 \}$ 
C)  domain : all real numbers
range: $\{ - 2 , - 1 \}$ 
D)  domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - 1,1 )$ 
E)  domain: $\{ - 2 , - 1 \}$
range: all real numbers 
A)  domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B)  domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $\{ - 2 , - 1 \}$ 
C)  domain : all real numbers
range: $\{ - 2 , - 1 \}$ 
D)  domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - 1,1 )$ 
E)  domain: $\{ - 2 , - 1 \}$
range: all real numbers

Question 17

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$y = \left| \frac { 7 } { 9 } x \right|$

Accepted Answer

A)  vertical shift of $\frac { 7 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 7 }$ units 
C)  vertical shrink of $\frac { 7 } { 9 }$ units 
D)  horizontal shrink of $\frac { 7 } { 9 }$ units vertical shift of $\frac { 9 } { 7 }$ units 
E)  horizontal shrink of $\frac { 7 } { 9 }$ units 
A)  vertical shift of $\frac { 7 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 7 }$ units 
C)  vertical shrink of $\frac { 7 } { 9 }$ units 
D)  horizontal shrink of $\frac { 7 } { 9 }$ units vertical shift of $\frac { 9 } { 7 }$ units 
E)  horizontal shrink of $\frac { 7 } { 9 }$ units

Question 18

Find $f \circ g$.
$f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Accepted Answer

A)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } + 6 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } + 1 } { x ^ { 2 } - 9 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 9 }$ 
E)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 23 } { x ^ { 2 } - 9 }$ 
A)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } + 6 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } + 1 } { x ^ { 2 } - 9 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 9 }$ 
E)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 23 } { x ^ { 2 } - 9 }$

Question 19

Find the slope and $y$-intercept of the equation of the line.
$y = - 2 x - 9$

Accepted Answer

A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: $- 9$ 
B)  slope: $- \frac { 1 } { 9 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: $- 9$ 
D)  slope: $- 9 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: 9 
A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: $- 9$ 
B)  slope: $- \frac { 1 } { 9 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: $- 9$ 
D)  slope: $- 9 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: 9

Question 20

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

Accepted Answer

A)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
B)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 + x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
E)  $\quad f ( x ) = 1 - \sqrt { 1 - x }$ 
A)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
B)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 + x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
E)  $\quad f ( x ) = 1 - \sqrt { 1 - x }$

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 3 x - 2 } { 5 }$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

Find the domain of the function. $f ( t ) = \sqrt { 64 - t ^ { 2 } }$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 11 x - 36$ $g ( x ) = - 7 x - 4$

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } - 1$

Which equation does not represent $y$ as a function of $x$ ?

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Use the graph of the function to find the domain and range of $f$ .

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 7 } { 9 } x \right|$

Find $f \circ g$ . $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Find the slope and $y$ -intercept of the equation of the line. $y = - 2 x - 9$

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

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

Exam 1: Functions and Their Graphs

Restrict the domain of the following function fff so that the function is one-to-one and has an inverse function. f(x)=−∣x−4∣+2f ( x ) = - | x - 4 | + 2f(x)=−∣x−4∣+2

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=−f(x−2)g ( x ) = - f ( x - 2 )g(x)=−f(x−2)

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−15(x+4)3g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }g(x)=−51​(x+4)3

Given the following function, h(x)h ( x )h(x) , find two functions fff and ggg such that (f∘g)(x)=h(x)( f \circ g ) ( x ) = h ( x )(f∘g)(x)=h(x) . h(x)=x2−113h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }h(x)=3x2−11​

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−12(x+9)3g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }g(x)=−21​(x+9)3

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=−3x−25f ( x ) = \frac { - 3 x - 2 } { 5 }f(x)=5−3x−2​

Find the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−13x+5g(x)=−9x+2f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2f(x)=x2−13x+5g(x)=−9x+2

Determine the domain of g(x)=1x2−81g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }g(x)=x2−811​ .

Find the domain of the function. f(t)=64−t2f ( t ) = \sqrt { 64 - t ^ { 2 } }f(t)=64−t2​

Find the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−11x−36f ( x ) = x ^ { 2 } - 11 x - 36f(x)=x2−11x−36 g(x)=−7x−4g ( x ) = - 7 x - 4g(x)=−7x−4

Find the inverse function of fff . f(x)=x5−1f ( x ) = x ^ { 5 } - 1f(x)=x5−1

Which equation does not represent yyy as a function of xxx ?

Graph the function and determine the interval(s) for which f(x)≥0f ( x ) \geq 0f(x)≥0 . f(x)=−x2+4xf ( x ) = - x ^ { 2 } + 4 xf(x)=−x2+4x

Use the graph of the function to find the domain and range of fff .

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣79x∣y = \left| \frac { 7 } { 9 } x \right|y=​97​x​

Find f∘gf \circ gf∘g . f(x)=x+3g(x)=4x2−9f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }f(x)=x+3g(x)=x2−94​

Find the slope and yyy -intercept of the equation of the line. y=−2x−9y = - 2 x - 9y=−2x−9

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

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

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 3 x - 2 } { 5 }$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

Find the domain of the function. $f ( t ) = \sqrt { 64 - t ^ { 2 } }$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 11 x - 36$ $g ( x ) = - 7 x - 4$

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } - 1$

Which equation does not represent $y$ as a function of $x$ ?

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Use the graph of the function to find the domain and range of $f$ .

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 7 } { 9 } x \right|$

Find $f \circ g$ . $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Find the slope and $y$ -intercept of the equation of the line. $y = - 2 x - 9$