Question 1

Write the slope-intercept form of the equation of the line through the given point parallel to the given line.
point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

Accepted Answer

A)  $y = - \frac { 1 } { 28 } x - \frac { 109 } { 28 }$ 
B)  $y = \frac { 1 } { 4 } x - \frac { 19 } { 4 }$ 
C)  $y = 28 x + 80$ 
D)  $y = - 4 x + 8$ 
E)  $y = - 4 x - 13$ 
A)  $y = - \frac { 1 } { 28 } x - \frac { 109 } { 28 }$ 
B)  $y = \frac { 1 } { 4 } x - \frac { 19 } { 4 }$ 
C)  $y = 28 x + 80$ 
D)  $y = - 4 x + 8$ 
E)  $y = - 4 x - 13$

Question 2

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 3

If $f$ is an even function, determine if $g$ is even, odd, or neither.
$$g ( x ) = f ( x + 4 )$$

Accepted Answer

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

Question 4

Algebraically determine whether the function below is even, odd, or neither.
$$f ( s ) = 8 s ^ { 7 / 6 }$$

Accepted Answer

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

Question 5

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$ 
$L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$

Accepted Answer

A)  parallel 
B)  perpendicular 
C)  neither 
A)  parallel 
B)  perpendicular 
C)  neither

Question 6

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 7

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)  $( - \infty , \infty )$

Question 8

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

Accepted Answer

A) 
domain : all real numbers
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B) 
domain : all real numbers
range : all real numbers 
C) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
D) 
domain : $( - \infty , - 2 ) \cup ( - 1 , \infty )$
range : $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
E) 
Domain: all real numbers
Range: $( - \infty , - 2 ] \cup [ - 1 , \infty )$ 
A) 
domain : all real numbers
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B) 
domain : all real numbers
range : all real numbers 
C) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range: $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
D) 
domain : $( - \infty , - 2 ) \cup ( - 1 , \infty )$
range : $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
E) 
Domain: all real numbers
Range: $( - \infty , - 2 ] \cup [ - 1 , \infty )$

Question 9

Does the table describe a function?
$\begin{array}{|c|c|c|c|c|c|}
\hline \text { Input value } & 5 & 10 & 13 & 10 & 5 \
\hline \text { Output value } & -13 & -9 & 0 & 9 & 13 \
\hline
\end{array}$

Accepted Answer

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

Question 10

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 11

Match the graph of the function shown below with the graph of its inverse function

Accepted Answer

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

Question 12

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 13

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) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+56\right)-56} & & \frac{8 x-7^{3}+7^{3}}{8} \
&=\sqrt[3]{x^{3}+56-56} & &=\frac{8 x}{8} \
&=\sqrt[3]{x^{3}} & &\
& =x&=x\
\end{aligned}$ 
B) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+7\right)-7} & &=\frac{8 x-7+7}{8} \
&=\sqrt[3]{x^{3}+7-7} & &=\frac{8 x}{8} \
&=\sqrt[3]{x^{3}} & \
&=x&=x\
\end{aligned}$ 
C) 
$\begin{array}{l}
\begin{array}{lll}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(\frac{8 x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{array}
\quad \quad 
\begin{array}{lll}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7+7}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
\
&=x
\end{array}
\end{array}$ 
D) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(8 x^{3}+56\right)-56} & &=\frac{8^{3} x-7^{3}+7^{3}}{8^{3}} \
&=\sqrt[3]{8 x^{3}+56-56} & & =\frac{8^{3} x}{8^{3}} \
&=\sqrt[3]{8 x^{3}} & & \
&=x & &=x 
\end{aligned}$ 
E) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+\frac{7}{8}\right)-7} & & =\frac{24 x-21+21}{24} \
&=\sqrt[3]{x^{3}+\frac{0}{8}} & & =\frac{24 x}{24} \
&=\sqrt[3]{x^{3}} & & =x \
&=x
\end{aligned}$ 
A) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+56\right)-56} & & \frac{8 x-7^{3}+7^{3}}{8} \
&=\sqrt[3]{x^{3}+56-56} & &=\frac{8 x}{8} \
&=\sqrt[3]{x^{3}} & &\
& =x&=x\
\end{aligned}$ 
B) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+7\right)-7} & &=\frac{8 x-7+7}{8} \
&=\sqrt[3]{x^{3}+7-7} & &=\frac{8 x}{8} \
&=\sqrt[3]{x^{3}} & \
&=x&=x\
\end{aligned}$ 
C) 
$\begin{array}{l}
\begin{array}{lll}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(\frac{8 x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{array}
\quad \quad 
\begin{array}{lll}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7+7}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
\
&=x
\end{array}
\end{array}$ 
D) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(8 x^{3}+56\right)-56} & &=\frac{8^{3} x-7^{3}+7^{3}}{8^{3}} \
&=\sqrt[3]{8 x^{3}+56-56} & & =\frac{8^{3} x}{8^{3}} \
&=\sqrt[3]{8 x^{3}} & & \
&=x & &=x 
\end{aligned}$ 
E) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} & g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\sqrt[3]{\left(x^{3}+\frac{7}{8}\right)-7} & & =\frac{24 x-21+21}{24} \
&=\sqrt[3]{x^{3}+\frac{0}{8}} & & =\frac{24 x}{24} \
&=\sqrt[3]{x^{3}} & & =x \
&=x
\end{aligned}$

Question 14

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 15

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 16

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 17

Estimate the slope of the line.

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B) 2 
C) $- 2$ 
D) $\frac { 1 } { 2 }$ 
E) $- 3$ 
A)  $- \frac { 1 } { 2 }$ 
B) 2 
C) $- 2$ 
D) $\frac { 1 } { 2 }$ 
E) $- 3$

Question 18

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 19

If $f$ is an even function, determine if $g$ is even, odd, or neither.
$$g ( x ) = f ( - x ) + 1$$

Accepted Answer

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

Question 20

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

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

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

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

Algebraically determine whether the function below is even, odd, or neither. $f ( s ) = 8 s ^ { 7 / 6 }$

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither. $L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$ $L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$

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

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

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

Does the table describe a function? Input value 5 10 13 10 5 Output value -13 -9 0 9 13

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

Match the graph of the function shown below with the graph of its inverse function

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

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

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

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

Estimate the slope of the line.

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

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( - x ) + 1$

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

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

Calculus Practice Problems

Filters

Exam 1: Functions and Their Graphs

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: (3,−4)( 3 , - 4 ) \quad(3,−4) line: 28x+7y=−428 x + 7 y = - 428x+7y=−4

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

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=f(x+4)g ( x ) = f ( x + 4 )g(x)=f(x+4)

Algebraically determine whether the function below is even, odd, or neither. f(s)=8s7/6f ( s ) = 8 s ^ { 7 / 6 }f(s)=8s7/6

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

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 .

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

Does the table describe a function? Input value 5 10 13 10 5 Output value -13 -9 0 9 13

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​

Match the graph of the function shown below with the graph of its inverse function

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

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 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​

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​

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)

Estimate the slope of the line.

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

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=f(−x)+1g ( x ) = f ( - x ) + 1g(x)=f(−x)+1

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)

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

Calculus Practice Problems

Filters

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

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

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

Algebraically determine whether the function below is even, odd, or neither. $f ( s ) = 8 s ^ { 7 / 6 }$

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

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

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

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

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

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

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

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

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( - x ) + 1$

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