Question 1

Find the domain of the given function.
-$$f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x - 1 }$$

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $[ - 3,1 ) \cup ( 1,3 ]$ 
C)  $[ - 9,1 ) \cup ( 1,9 ]$ 
D)  $[ - 3,3 ]$ 
A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $[ - 3,1 ) \cup ( 1,3 ]$ 
C)  $[ - 9,1 ) \cup ( 1,9 ]$ 
D)  $[ - 3,3 ]$

Question 2

Describe how to transform the graph of f into the graph of g.
-$f ( x ) = | 4 x |$ and $g ( x ) = 2 | x |$

Accepted Answer

A)  Vertically stretch the graph of $f$ by a factor of 4 and horizontally shrink by a factor of $\frac { 1 } { 2 }$. 
B)  Horizontally stretch the graph of $f$ by a factor of 4 and vertically stretch by a factor of 2 . 
C)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 4 }$ and vertically stretch by a factor of $2 .$ 
D)  Vertically stretch the graph by a factor of $4 + 2$. 
A)  Vertically stretch the graph of $f$ by a factor of 4 and horizontally shrink by a factor of $\frac { 1 } { 2 }$. 
B)  Horizontally stretch the graph of $f$ by a factor of 4 and vertically stretch by a factor of 2 . 
C)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 4 }$ and vertically stretch by a factor of $2 .$ 
D)  Vertically stretch the graph by a factor of $4 + 2$.

Question 3

Fill in the blanks to complete the statement.
-The graph of $y = - 0.2 \sqrt [ 3 ] { - x }$ can be obtained from the graph of $y = \sqrt [ 3 ] { x }$ by reflecting across the   -axis, shrinking vertically by a factor   and then reflecting across the    -axis.

Accepted Answer

A)  $\mathrm { x } ; 0.2 ; \mathrm { x }$ 
B)  $y ; 0.2 ; x$ 
C)  $y ; - 0.2 ; x$ 
D)  $x ; - 0.2 ; y$ 
A)  $\mathrm { x } ; 0.2 ; \mathrm { x }$ 
B)  $y ; 0.2 ; x$ 
C)  $y ; - 0.2 ; x$ 
D)  $x ; - 0.2 ; y$

Question 4

Find the asymptote(s) of the given function.
-$f ( x ) = 3.1 ^ { x }$ horizontal asymptotes(s)

Accepted Answer

A)  $y = 3.1$ 
B)  None 
C)  $x = 0$ 
D)  $y = 0$ 
A)  $y = 3.1$ 
B)  None 
C)  $x = 0$ 
D)  $y = 0$

Question 5

Solve the problem.
-The following information pertains to a bakery which makes donuts.

Make a scatterplot of the data. Then graph the following two functions on the same coordinate system: $\mathrm { f } _ { 1 } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 100 \mathrm { x } ; \mathrm { f } _ { 2 } ( \mathrm { x } ) = 85 \mathrm { x }$. Decide which function best models the data, and then use that function to estimate the profit associated with making 35 cases of donuts.

Accepted Answer

A)  $\mathrm { f } _ { 2 }$; Profit for 35 cases is $\$ 2975$. 
B)  $\mathrm { f } _ { 1 }$; Profit for 35 cases is $\$ 2275$. 
C)  $\mathrm { f } _ { 1 }$; Profit for 35 cases is $\$ 2625$. 
D)  $\mathrm { f } _ { 2 }$; Profit for 35 cases is $\$ 3525 .$ 
A)  $\mathrm { f } _ { 2 }$; Profit for 35 cases is $\$ 2975$. 
B)  $\mathrm { f } _ { 1 }$; Profit for 35 cases is $\$ 2275$. 
C)  $\mathrm { f } _ { 1 }$; Profit for 35 cases is $\$ 2625$. 
D)  $\mathrm { f } _ { 2 }$; Profit for 35 cases is $\$ 3525 .$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Graph the piecewise-defined function.
-$$g ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } & \text { if } x \leq 0 \
e ^ { x } & \text { if } x > 0
\end{array} \right.$$

Accepted Answer

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

Question 7

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-

Accepted Answer

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

Question 8

Find a direct relationship between x and y.
-$x = 9 t ^ { 2 }$ and $y = t + 2$

Accepted Answer

A)  $x = 9 y ^ { 2 } - 36 y + 36$ 
B)  $y = \frac { \sqrt { x } } { 3 } + 2$ 
C)  $x = 9 y ^ { 2 } + 36 y + 36$ 
D)  $y = 3 x + 2$ 
A)  $x = 9 y ^ { 2 } - 36 y + 36$ 
B)  $y = \frac { \sqrt { x } } { 3 } + 2$ 
C)  $x = 9 y ^ { 2 } + 36 y + 36$ 
D)  $y = 3 x + 2$

Question 9

Graph the function on your calculator to determine the domain and range from the graph.
-$$p ( x ) = ( x + 7 ) ^ { 2 }$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $[ \langle a \rangle , \infty )$ 
B)  Domain: $[ - 7 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
A)  Domain: $( - \infty , \infty )$; range: $[ \langle a \rangle , \infty )$ 
B)  Domain: $[ - 7 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$

Question 10

Solve the problem.
-The following data set gives the average home value, in dollars, for a city at 5 -year intervals.

In which 5 -year period did average home value change the most?

Accepted Answer

A)  2000-2005 
B)  $1985 - 1990$ 
C)  $1995 - 2000$ 
D)  $1990 - 1995$ 
A)  2000-2005 
B)  $1985 - 1990$ 
C)  $1995 - 2000$ 
D)  $1990 - 1995$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The area of a rectangle whose length is 15 more than its width $x$

Accepted Answer

A)  $( x + 15 ) ( x )$ 
B)  $2 x + 15$ 
C)  $( x ) ( x - 15 )$ 
D)  $2 \left( x ^ { 2 } + 15 x \right)$ 
A)  $( x + 15 ) ( x )$ 
B)  $2 x + 15$ 
C)  $( x ) ( x - 15 )$ 
D)  $2 \left( x ^ { 2 } + 15 x \right)$

Question 12

Find the inverse of the function.
-$$f ( x ) = \frac { 8 x + 1 } { - 5 x - 4 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 5 \mathrm { x } - 8 } { 4 \mathrm { x } + 1 }$ 
B)  $f ^ { 1 } ( x ) = \frac { 4 x + 1 } { - 5 x - 8 }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { 8 x + 1 } { - 5 x - 4 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 5 \mathrm { x } - 8 } { 4 \mathrm { x } + 1 }$ 
B)  $f ^ { 1 } ( x ) = \frac { 4 x + 1 } { - 5 x - 8 }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { 8 x + 1 } { - 5 x - 4 }$

Question 13

Write the word or phrase that best completes each statement or answers the question.
Sketch the graph of the given function based on the graph of the function f given below.
-$$\text { Sketch the graph of } y = 1 + 2 f ( x - 1 ) \text {. }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Find the asymptote(s) of the given function.
-$g ( x ) = \frac { x - 2 } { ( x - 2 ) ( x + 5 ) }$ vertical asymptotes(s)

Accepted Answer

A)  $x = - 2$ 
B)  $x = - 2 , x = 5$ 
C)  $x = 2 , x = - 5$ 
D)  $x = 2$ 
A)  $x = - 2$ 
B)  $x = - 2 , x = 5$ 
C)  $x = 2 , x = - 5$ 
D)  $x = 2$

Question 15

Identify which of the twelve basic functions listed below fit the description given.
-The three functions with end behavior $\lim _ { x \rightarrow \infty } f ( x ) = - \infty$

Accepted Answer

A)  $y = x , y = \frac { 1 } { 1 + e ^ { - x } } , y = \operatorname { int } ( x )$ 
B)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
C)  $y = x , y = x ^ { 3 } , y = \operatorname { int } ( x )$ 
D)  $y = x ^ { 2 } , y = x ^ { 3 } , y = \operatorname { int } ( x )$ 
A)  $y = x , y = \frac { 1 } { 1 + e ^ { - x } } , y = \operatorname { int } ( x )$ 
B)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
C)  $y = x , y = x ^ { 3 } , y = \operatorname { int } ( x )$ 
D)  $y = x ^ { 2 } , y = x ^ { 3 } , y = \operatorname { int } ( x )$

Question 16

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.
-$$f ( x ) = \frac { x + 8 } { x - 7 } \text { and } g ( x ) = \frac { 7 x + 8 } { x - 1 }$$

Accepted Answer

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

Question 17

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
-$$y = | 5 x + 10 |$$

Accepted Answer

A)  $f ( x ) = | - x | , g ( x ) = 5 x - 10$ 
B)  $f ( x ) = x , g ( x ) = 5 x + 10$ 
C)  $f ( x ) = - | x | , g ( x ) = 5 x + 10$ 
D)  $f ( x ) = | x | , g ( x ) = 5 x + 10$ 
A)  $f ( x ) = | - x | , g ( x ) = 5 x - 10$ 
B)  $f ( x ) = x , g ( x ) = 5 x + 10$ 
C)  $f ( x ) = - | x | , g ( x ) = 5 x + 10$ 
D)  $f ( x ) = | x | , g ( x ) = 5 x + 10$

Question 18

Identify which of the twelve basic functions listed below fit the description given.
-The four functions whose graphs look the same turned upside down

Accepted Answer

A)  $y = \sin x , y = \cos x , y = x , y = x ^ { 3 }$ 
B)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \sin x$ 
C)  $y = x , y = \frac { 1 } { x } , y = \sin x , y = \frac { 1 } { 1 + e ^ { - x } }$ 
D)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \cos x$ 
A)  $y = \sin x , y = \cos x , y = x , y = x ^ { 3 }$ 
B)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \sin x$ 
C)  $y = x , y = \frac { 1 } { x } , y = \sin x , y = \frac { 1 } { 1 + e ^ { - x } }$ 
D)  $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \cos x$

Question 19

Give the equation of the function g whose graph is described.
-The graph of $f ( x ) = | x |$ is vertically stretched by a factor of $4.8$. This graph is then reflected across the $x$-axis. Finally, the graph is shifted $0.52$ units downward.

Accepted Answer

A)  $g ( x ) = 4.8 | - x | - 0.52$ 
B)  $g ( x ) = 4.8 | x | - 0.52$ 
C)  $g ( x ) = - 4.8 | x | - 0.52$ 
D)  $g ( x ) = 4.8 | x - 0.52 |$ 
A)  $g ( x ) = 4.8 | - x | - 0.52$ 
B)  $g ( x ) = 4.8 | x | - 0.52$ 
C)  $g ( x ) = - 4.8 | x | - 0.52$ 
D)  $g ( x ) = 4.8 | x - 0.52 |$

Question 20

Use an equation to solve the problem.
-One positive number is twice another positive number. The sum of the two numbers is 360 . Find the two numbers.

Accepted Answer

A)  180,180 
B)  120,122 
C)  120,240 
D)  60,300 
A)  180,180 
B)  120,122 
C)  120,240 
D)  60,300

Find the domain of the given function. - $f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x - 1 }$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = | 4 x |$ and $g ( x ) = 2 | x |$

Find the asymptote(s) of the given function. - $f ( x ) = 3.1 ^ { x }$ horizontal asymptotes(s)

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Find a direct relationship between x and y. - $x = 9 t ^ { 2 }$ and $y = t + 2$

Graph the function on your calculator to determine the domain and range from the graph. - $p ( x ) = ( x + 7 ) ^ { 2 }$

Solve the problem. -The following data set gives the average home value, in dollars, for a city at 5 -year intervals. In which 5 -year period did average home value change the most?

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The area of a rectangle whose length is 15 more than its width $x$

Find the inverse of the function. - $f ( x ) = \frac { 8 x + 1 } { - 5 x - 4 }$

Find the asymptote(s) of the given function. - $g ( x ) = \frac { x - 2 } { ( x - 2 ) ( x + 5 ) }$ vertical asymptotes(s)

Identify which of the twelve basic functions listed below fit the description given. -The three functions with end behavior $\lim _ { x \rightarrow \infty } f ( x ) = - \infty$

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. - $f ( x ) = \frac { x + 8 } { x - 7 } \text { and } g ( x ) = \frac { 7 x + 8 } { x - 1 }$

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = | 5 x + 10 |$

Identify which of the twelve basic functions listed below fit the description given. -The four functions whose graphs look the same turned upside down

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = | x |$ is vertically stretched by a factor of $4.8$ . This graph is then reflected across the $x$ -axis. Finally, the graph is shifted $0.52$ units downward.

Use an equation to solve the problem. -One positive number is twice another positive number. The sum of the two numbers is 360 . Find the two numbers.

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 the domain of the given function. - f(x)=9−x2x−1f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x - 1 }f(x)=x−19−x2​​

Describe how to transform the graph of f into the graph of g. - f(x)=∣4x∣f ( x ) = | 4 x |f(x)=∣4x∣ and g(x)=2∣x∣g ( x ) = 2 | x |g(x)=2∣x∣

Find the asymptote(s) of the given function. - f(x)=3.1xf ( x ) = 3.1 ^ { x }f(x)=3.1x horizontal asymptotes(s)