Question 1

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
-$$y = \frac { 1 } { x ^ { 2 } - 4 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 4 } , g ( x ) = x ^ { 2 } - 4$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 4$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 4$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - 1 / 4$ 
A)  $f ( x ) = \frac { 1 } { 4 } , g ( x ) = x ^ { 2 } - 4$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 4$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 4$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - 1 / 4$

Question 2

Give the equation of the function g whose graph is described.
-The graph of $f ( x ) = 6 \sqrt { x - 1 } + 5$ is reflected across the $x$-axis .

Accepted Answer

A)  $g ( x ) = - 6 \sqrt { x - 1 } + 5$ 
B)  $g ( x ) = 6 \sqrt { - x - 1 } + 5$ 
C)  $g ( x ) = 6 \sqrt { - x - 1 } - 5$ 
D)  $g ( x ) = - 6 \sqrt { x - 1 } - 5$ 
A)  $g ( x ) = - 6 \sqrt { x - 1 } + 5$ 
B)  $g ( x ) = 6 \sqrt { - x - 1 } + 5$ 
C)  $g ( x ) = 6 \sqrt { - x - 1 } - 5$ 
D)  $g ( x ) = - 6 \sqrt { x - 1 } - 5$

Question 3

Match the function with the graph.
-

Accepted Answer

A)  $y = - \frac { 1 } { x } - 1$ 
B)  $y = - \frac { 1 } { x } + 1$ 
C)  $y = - \frac { 1 } { x }$ 
D)  $y = \frac { 1 } { x } - 1$ 
A)  $y = - \frac { 1 } { x } - 1$ 
B)  $y = - \frac { 1 } { x } + 1$ 
C)  $y = - \frac { 1 } { x }$ 
D)  $y = \frac { 1 } { x } - 1$

Question 4

Solve the problem.
-Use the graph of $\mathrm { f }$ to estimate the local maximum and local minimum.

Accepted Answer

A)  Local maximum: $\infty$; local minimum: $- \infty$ 
B)  No local maximum; no local minimum 
C)  Local maximum: approx. 3.66; local minimum: approx. $- 2.55$ 
D)  Local maximum: 1 ; local minimum: 4 
A)  Local maximum: $\infty$; local minimum: $- \infty$ 
B)  No local maximum; no local minimum 
C)  Local maximum: approx. 3.66; local minimum: approx. $- 2.55$ 
D)  Local maximum: 1 ; local minimum: 4

Question 5

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The total cost if $\$ 20,000$ plus $\$ 6.35$ for each item produced.

Accepted Answer

A)  $\$ ( 20,000 + 6.35 x )$ 
B)  $\$ ( 20,000 - 6.35 x )$ 
C)  $\$ ( 20,000 + 6.35 ) x$ 
D)  $\$ ( 20,000 x + 6.35 )$ 
A)  $\$ ( 20,000 + 6.35 x )$ 
B)  $\$ ( 20,000 - 6.35 x )$ 
C)  $\$ ( 20,000 + 6.35 ) x$ 
D)  $\$ ( 20,000 x + 6.35 )$

Question 6

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding
the x-intercepts.
-$7 x-6=\sqrt{x+9}$

Accepted Answer

A)  $- 9$ 
B)  $0.4$ 
C)  $- 1.3$ 
D)  $1.3$ 
A)  $- 9$ 
B)  $0.4$ 
C)  $- 1.3$ 
D)  $1.3$

Question 7

Find the (x,y) pair for the value of the parameter.
-$x = t ^ { 3 } - 6 t$ and $y = \sqrt { t - 1 }$ for $t = 10$

Accepted Answer

A)  $( 9,1060 )$ 
B)  $( 3,940 )$ 
C)  $( 940,3 )$ 
D)  $( 1060,3 )$ 
A)  $( 9,1060 )$ 
B)  $( 3,940 )$ 
C)  $( 940,3 )$ 
D)  $( 1060,3 )$

Question 8

Determine if the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 9

Perform the requested operation or operations.
-$f ( x ) = \sqrt { x + 4 } ; g ( x ) = 8 x - 8$, find $f ( g ( x ) )$.

Accepted Answer

A)  $f ( g ( x ) ) = 2 \sqrt { 2 x - 1 }$ 
B)  $f ( g ( x ) ) = 8 \sqrt { x - 4 }$ 
C)  $f ( g ( x ) ) = 2 \sqrt { 2 x + 1 }$ 
D)  $f ( g ( x ) ) = 8 \sqrt { x + 4 } - 8$ 
A)  $f ( g ( x ) ) = 2 \sqrt { 2 x - 1 }$ 
B)  $f ( g ( x ) ) = 8 \sqrt { x - 4 }$ 
C)  $f ( g ( x ) ) = 2 \sqrt { 2 x + 1 }$ 
D)  $f ( g ( x ) ) = 8 \sqrt { x + 4 } - 8$

Question 10

Determine whether the formula determines y as a function of x.
-$$y = x ^ { 2 } - 6$$

Accepted Answer

A) True 
 B)False

Question 11

Perform the requested operation or operations.
-$$f ( x ) = 4 x + 10 ; g ( x ) = 3 x - 1$$
Find $f ( g ( x ) )$.

Accepted Answer

A)  $f ( g ( x ) ) = 12 x + 9$ 
B)  $f ( g ( x ) ) = 12 x + 6$ 
C)  $f ( g ( x ) ) = 12 x + 29$ 
D)  $f ( g ( x ) ) = 12 x + 14$ 
A)  $f ( g ( x ) ) = 12 x + 9$ 
B)  $f ( g ( x ) ) = 12 x + 6$ 
C)  $f ( g ( x ) ) = 12 x + 29$ 
D)  $f ( g ( x ) ) = 12 x + 14$

Question 12

Write the specified quantity as a function of the specified variable.
-The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Accepted Answer

A)  $A = 7 b$ 
B)  $\mathrm { A } = \frac { 15 } { 16 } \mathrm {~b} ^ { 3 }$ 
C)  $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$ 
D)  $A = \frac { 15 } { 16 } b ^ { 2 }$ 
A)  $A = 7 b$ 
B)  $\mathrm { A } = \frac { 15 } { 16 } \mathrm {~b} ^ { 3 }$ 
C)  $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$ 
D)  $A = \frac { 15 } { 16 } b ^ { 2 }$

Question 13

Write the specified quantity as a function of the specified variable.
-The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.

Accepted Answer

A)  $V = \pi r ^ { 3 }$ 
B)  $V = 4 \pi r$ 
C)  $V = 2 \pi r ^ { 3 }$ 
D)  $V = \frac { 1 } { 2 } \pi r ^ { 3 }$ 
A)  $V = \pi r ^ { 3 }$ 
B)  $V = 4 \pi r$ 
C)  $V = 2 \pi r ^ { 3 }$ 
D)  $V = \frac { 1 } { 2 } \pi r ^ { 3 }$

Question 14

Describe how to transform the graph of f into the graph of g.
-$$f ( x ) = x ^ { 3 } \text { and } g ( x ) = - x ^ { 3 }$$

Accepted Answer

A)  Reflect the graph of $f$ across the $x$-axis. 
B)  Shift the graph of $f$ down 1 unit. 
C)  Reflect the graph of $f$ across the $y$-axis. 
D)  Reflect the graph of $f$ across the $x$-axis and then reflect across the $y$-axis. 
A)  Reflect the graph of $f$ across the $x$-axis. 
B)  Shift the graph of $f$ down 1 unit. 
C)  Reflect the graph of $f$ across the $y$-axis. 
D)  Reflect the graph of $f$ across the $x$-axis and then reflect across the $y$-axis.

Question 15

Solve the equation algebraically.
-$$6 \sqrt { x } + x = 3$$

Accepted Answer

A)  $21 - 12 \sqrt { 3 }$ 
B)  $221 \pm 212 \sqrt { 3 }$ 
C)  $21 \pm 12 \sqrt { 3 }$ 
D)  $- 21 \pm 12 \sqrt { 3 }$ 
A)  $21 - 12 \sqrt { 3 }$ 
B)  $221 \pm 212 \sqrt { 3 }$ 
C)  $21 \pm 12 \sqrt { 3 }$ 
D)  $- 21 \pm 12 \sqrt { 3 }$

Question 16

Perform the requested operation or operations.
-$$f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6$$
Find $f ( g ( x ) )$.

Accepted Answer

A)  $f ( g ( x ) ) = 2 \sqrt { 2 x - 1 }$ 
B)  $f ( g ( x ) ) = 8 \sqrt { x - 4 }$ 
C)  $f ( g ( x ) ) = 2 \sqrt { 2 x + 1 }$ 
D)  $f ( g ( x ) ) = 8 \sqrt { x + 2 } - 6$ 
A)  $f ( g ( x ) ) = 2 \sqrt { 2 x - 1 }$ 
B)  $f ( g ( x ) ) = 8 \sqrt { x - 4 }$ 
C)  $f ( g ( x ) ) = 2 \sqrt { 2 x + 1 }$ 
D)  $f ( g ( x ) ) = 8 \sqrt { x + 2 } - 6$

Question 17

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-$$y _ { 1 } = | x | y _ { 2 } = - 2 | x |$$

Accepted Answer

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

Question 18

Describe how to transform the graph of f into the graph of g.
-$f ( x ) = \sqrt { x }$ and $g ( x ) = 6 \sqrt { x }$

Accepted Answer

A)  Horizontally stretch the graph of $f$ by a factor of 6 . 
B)  Vertically stretch the graph of $\mathrm { f }$ by a factor of $6 .$ 
C)  Vertically shrink the graph of $\mathrm { f }$ by a factor of $\frac { 1 } { 6 }$. 
D)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 6 }$. 
A)  Horizontally stretch the graph of $f$ by a factor of 6 . 
B)  Vertically stretch the graph of $\mathrm { f }$ by a factor of $6 .$ 
C)  Vertically shrink the graph of $\mathrm { f }$ by a factor of $\frac { 1 } { 6 }$. 
D)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 6 }$.

Question 19

Match the function with the graph.
-

Accepted Answer

A)  $y = - \ln ( x - 3 )$ 
B)  $y = \ln x + 3$ 
C)  $y = - \ln ( x + 3 )$ 
D)  $y = - \ln ( x )$ 
A)  $y = - \ln ( x - 3 )$ 
B)  $y = \ln x + 3$ 
C)  $y = - \ln ( x + 3 )$ 
D)  $y = - \ln ( x )$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
-$$f ( x ) = \frac { 2 } { x } \text { and } g ( x ) = \frac { 2 } { x }$$

Accepted Answer

\[\begin{array} { l } 
f ( g ( x ) ) = \

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = \frac { 1 } { x ^ { 2 } - 4 }$

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = 6 \sqrt { x - 1 } + 5$ is reflected across the $x$ -axis .

Match the function with the graph. -

Solve the problem. -Use the graph of $\mathrm { f }$ to estimate the local maximum and local minimum. $Solve the problem. -Use the graph of \mathrm { f } to estimate the local maximum and local minimum.$

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The total cost if $\$ 20,000$ plus $\$ 6.35$ for each item produced.

Find the (x,y) pair for the value of the parameter. - $x = t ^ { 3 } - 6 t$ and $y = \sqrt { t - 1 }$ for $t = 10$

Determine if the function is one-to-one. -

Perform the requested operation or operations. - $f ( x ) = \sqrt { x + 4 } ; g ( x ) = 8 x - 8$ , find $f ( g ( x ) )$ .

Determine whether the formula determines y as a function of x. - $y = x ^ { 2 } - 6$

Perform the requested operation or operations. - $f ( x ) = 4 x + 10 ; g ( x ) = 3 x - 1$ Find $f ( g ( x ) )$ .

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Write the specified quantity as a function of the specified variable. -The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.

Describe how to transform the graph of f into the graph of g. - $f ( x ) = x ^ { 3 } \text { and } g ( x ) = - x ^ { 3 }$

Solve the equation algebraically. - $6 \sqrt { x } + x = 3$

Perform the requested operation or operations. - $f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6$ Find $f ( g ( x ) )$ .

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = 6 \sqrt { x }$

Match the function with the graph. -

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = \frac { 2 } { x } \text { and } g ( x ) = \frac { 2 } { x }$

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - y=1x2−4y = \frac { 1 } { x ^ { 2 } - 4 }y=x2−41​

Give the equation of the function g whose graph is described. -The graph of f(x)=6x−1+5f ( x ) = 6 \sqrt { x - 1 } + 5f(x)=6x−1​+5 is reflected across the xxx -axis .

Match the function with the graph. -

Solve the problem. -Use the graph of f\mathrm { f }f to estimate the local maximum and local minimum.

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The total cost if $20,000\$ 20,000$20,000 plus $6.35\$ 6.35$6.35 for each item produced.

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - 7x−6=x+97 x-6=\sqrt{x+9}7x−6=x+9​

Find the (x,y) pair for the value of the parameter. - x=t3−6tx = t ^ { 3 } - 6 tx=t3−6t and y=t−1y = \sqrt { t - 1 }y=t−1​ for t=10t = 10t=10

Determine if the function is one-to-one. -

Perform the requested operation or operations. - f(x)=x+4;g(x)=8x−8f ( x ) = \sqrt { x + 4 } ; g ( x ) = 8 x - 8f(x)=x+4​;g(x)=8x−8 , find f(g(x))f ( g ( x ) )f(g(x)) .

Determine whether the formula determines y as a function of x. - y=x2−6y = x ^ { 2 } - 6y=x2−6

Perform the requested operation or operations. - f(x)=4x+10;g(x)=3x−1f ( x ) = 4 x + 10 ; g ( x ) = 3 x - 1f(x)=4x+10;g(x)=3x−1 Find f(g(x))f ( g ( x ) )f(g(x)) .

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Write the specified quantity as a function of the specified variable. -The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.

Describe how to transform the graph of f into the graph of g. - f(x)=x3 and g(x)=−x3f ( x ) = x ^ { 3 } \text { and } g ( x ) = - x ^ { 3 }f(x)=x3 and g(x)=−x3

Solve the equation algebraically. - 6x+x=36 \sqrt { x } + x = 36x​+x=3

Perform the requested operation or operations. - f(x)=x+2;g(x)=8x−6f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6f(x)=x+2​;g(x)=8x−6 Find f(g(x))f ( g ( x ) )f(g(x)) .

Describe how to transform the graph of f into the graph of g. - f(x)=xf ( x ) = \sqrt { x }f(x)=x​ and g(x)=6xg ( x ) = 6 \sqrt { x }g(x)=6x​

Match the function with the graph. -

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - f(x)=2x and g(x)=2xf ( x ) = \frac { 2 } { x } \text { and } g ( x ) = \frac { 2 } { x }f(x)=x2​ and g(x)=x2​

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = \frac { 1 } { x ^ { 2 } - 4 }$

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = 6 \sqrt { x - 1 } + 5$ is reflected across the $x$ -axis .

Solve the problem. -Use the graph of $\mathrm { f }$ to estimate the local maximum and local minimum. $Solve the problem. -Use the graph of \mathrm { f } to estimate the local maximum and local minimum.$

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The total cost if $\$ 20,000$ plus $\$ 6.35$ for each item produced.

Find the (x,y) pair for the value of the parameter. - $x = t ^ { 3 } - 6 t$ and $y = \sqrt { t - 1 }$ for $t = 10$

Perform the requested operation or operations. - $f ( x ) = \sqrt { x + 4 } ; g ( x ) = 8 x - 8$ , find $f ( g ( x ) )$ .

Determine whether the formula determines y as a function of x. - $y = x ^ { 2 } - 6$

Perform the requested operation or operations. - $f ( x ) = 4 x + 10 ; g ( x ) = 3 x - 1$ Find $f ( g ( x ) )$ .

Describe how to transform the graph of f into the graph of g. - $f ( x ) = x ^ { 3 } \text { and } g ( x ) = - x ^ { 3 }$

Solve the equation algebraically. - $6 \sqrt { x } + x = 3$

Perform the requested operation or operations. - $f ( x ) = \sqrt { x + 2 } ; g ( x ) = 8 x - 6$ Find $f ( g ( x ) )$ .

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = 6 \sqrt { x }$

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = \frac { 2 } { x } \text { and } g ( x ) = \frac { 2 } { x }$