Question 1

Solve the problem.
-Estimate graphically the local maximum and local minimum of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } - 3 x$.

Accepted Answer

A)  Local maximum: 8.53; local minimum: $- 2.01$ 
B)  Local maximum: $1.67$; local minimum: $- 9$ 
C)  Local maximum: 9; local minimum: $- 1.67$ 
D)  Local maximum: 9; local minimum: $1.06$ 
A)  Local maximum: 8.53; local minimum: $- 2.01$ 
B)  Local maximum: $1.67$; local minimum: $- 9$ 
C)  Local maximum: 9; local minimum: $- 1.67$ 
D)  Local maximum: 9; local minimum: $1.06$

Question 2

Match the numerical model to the corresponding model.
-$\begin{array}{r|rrrrrr}
x & 0 & 3 & 8 & 15 & 24 & 35 \
\hline y & 1 & 2 & 3 & 4 & 5 & 6
\end{array}$

Accepted Answer

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

Question 3

Fill in the blanks to complete the statement.
-The graph of $y = - 5 x ^ { 3 } + 2$ can be obtained from the graph of $y = x ^ { 3 }$ by vertically stretching by a factor of ? reflecting across the $?$-axis, and shifting vertically $?$ units in the $?$ direction.

Accepted Answer

A)  $5 ; x ; 2$; upward 
B)  $2 ; x ; 5 ;$ upward 
C)  $5 ; y ; 2$; upward 
D)  $- 5 ; x ; 2$; downward 
A)  $5 ; x ; 2$; upward 
B)  $2 ; x ; 5 ;$ upward 
C)  $5 ; y ; 2$; upward 
D)  $- 5 ; x ; 2$; downward

Question 4

Match the equation with the appropriate graph.
-$$f ( x ) = \frac { 18 } { x ^ { 2 } - 9 }$$

Accepted Answer

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

Question 5

Match the numerical model to the corresponding model.
-

Accepted Answer

A)  $y = 7 x - 7$ 
B)  $y = 5 x - 1$ 
C)  $y = 3 x + 5$ 
D)  $y = 6 x - 4$ 
A)  $y = 7 x - 7$ 
B)  $y = 5 x - 1$ 
C)  $y = 3 x + 5$ 
D)  $y = 6 x - 4$

Question 6

Match the function with the graph.
-

Accepted Answer

A)  $y = | x - 1 | + 3$ 
B)  $y = | x + 1 |$ 
C)  $y = | x | - 1$ 
D)  $y = | x - 1 |$ 
A)  $y = | x - 1 | + 3$ 
B)  $y = | x + 1 |$ 
C)  $y = | x | - 1$ 
D)  $y = | x - 1 |$

Question 7

Describe how to transform the graph of f into the graph of g.
-$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt { 0.1 x }$

Accepted Answer

A)  Horizontally stretch the graph of $\mathrm { f }$ by a factor of 10 . 
B)  Vertically stretch the graph of $f$ by a factor of 10 . 
C)  Horizontally shrink the graph of $f$ by a factor of 10 . 
D)  Vertically shrink the graph of $f$ by a factor of 10 . 
A)  Horizontally stretch the graph of $\mathrm { f }$ by a factor of 10 . 
B)  Vertically stretch the graph of $f$ by a factor of 10 . 
C)  Horizontally shrink the graph of $f$ by a factor of 10 . 
D)  Vertically shrink the graph of $f$ by a factor of 10 .

Question 8

Determine whether the formula determines y as a function of x.
-$$y = 15$$

Accepted Answer

A) True 
 B)False

Question 9

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: $f _ { 1 } ( x ) = - x ^ { 2 } + 100 x ; f _ { 2 } ( x ) = - x ^ { 2 } + 80 x + 200$. Decide which function best models the data, and then use that function to estimate the maximum possible profit.

Accepted Answer

A)  $\mathrm { f } _ { 1 }$; maximum profit is $\$ 2500 .$ 
B)  $\mathrm { f } _ { 2 } ;$ maximum profit is $\$ 1800 .$ 
C)  $\mathrm { f } _ { 1 }$; maximum profit is $\$ 2900$. 
D)  $\mathrm { f } _ { 2 } ;$ maximum profit is $\$ 2670 .$ 
A)  $\mathrm { f } _ { 1 }$; maximum profit is $\$ 2500 .$ 
B)  $\mathrm { f } _ { 2 } ;$ maximum profit is $\$ 1800 .$ 
C)  $\mathrm { f } _ { 1 }$; maximum profit is $\$ 2900$. 
D)  $\mathrm { f } _ { 2 } ;$ maximum profit is $\$ 2670 .$

Question 10

Describe how to transform the graph of f into the graph of g.
-$f ( x ) = \sqrt { x }$ and $g ( x ) = - \sqrt { x + 4 }$

Accepted Answer

A)  Shift the graph of $f$ right 4 units and then reflect across the $x$-axis. 
B)  Shift the graph of $f$ left 4 units and then reflect across the $x$-axis. 
C)  Shift the graph of $f$ left 4 units and then reflect across the $y$-axis. 
D)  Shift the graph of $f$ up 4 units and then reflect across the $y$-axis. 
A)  Shift the graph of $f$ right 4 units and then reflect across the $x$-axis. 
B)  Shift the graph of $f$ left 4 units and then reflect across the $x$-axis. 
C)  Shift the graph of $f$ left 4 units and then reflect across the $y$-axis. 
D)  Shift the graph of $f$ up 4 units and then reflect across the $y$-axis.

Question 11

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

Accepted Answer

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

Question 12

Find the inverse of the function.
-$$f ( x ) = \sqrt { 2 x + 1 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { ( x - 1 ) ^ { 2 } } { 2 }$ for $x \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 2 } - 1$ for $x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 \mathrm { x } - 1 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } ^ { 2 } - 1 } { 2 }$ for $x \geq 0$ 
A)  $f ^ { - 1 } ( x ) = \frac { ( x - 1 ) ^ { 2 } } { 2 }$ for $x \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 2 } - 1$ for $x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 \mathrm { x } - 1 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } ^ { 2 } - 1 } { 2 }$ for $x \geq 0$

Question 13

Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = 4 x + 8 , g ( x ) = 4 x ^ { 2 }$$
Find $( f + g ) ( x )$.

Accepted Answer

A)  $4 x + 8 + 4 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
B)  $4 x + 8 - 4 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
C)  $\frac { 4 x + 8 } { 4 x ^ { 2 } } ;$ domain: $( - \infty , \infty )$ 
D)  $16 x ^ { 3 } + 32 x$; domain: $( - \infty , \infty )$ 
A)  $4 x + 8 + 4 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
B)  $4 x + 8 - 4 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
C)  $\frac { 4 x + 8 } { 4 x ^ { 2 } } ;$ domain: $( - \infty , \infty )$ 
D)  $16 x ^ { 3 } + 32 x$; domain: $( - \infty , \infty )$

Question 14

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions.
-Graph f $+ g$.

Accepted Answer

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

Question 15

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

Determine where $f$ is increasing or decreasing.

Accepted Answer

A)  $f$ is decreasing for the given $x$ values. 
B)  $f$ is increasing for the given $x$-values. 
C)  $f$ is constant for the given $x$-values. 
D)  $f$ is increasing until 1980, then $f$ is decreasing for remainder of $x$-values. 
A)  $f$ is decreasing for the given $x$ values. 
B)  $f$ is increasing for the given $x$-values. 
C)  $f$ is constant for the given $x$-values. 
D)  $f$ is increasing until 1980, then $f$ is decreasing for remainder of $x$-values.

Question 16

Write the specified quantity as a function of the specified variable.
-A square is inscribed in a circle. Write the area of the square as a function of the radius.

Accepted Answer

A)  $A = r$ 
B)  $A = 2 r$ 
C)  $\mathrm { A } = 2 \mathrm { r } ^ { 2 }$ 
D)  $A = 4 r ^ { 2 }$ 
A)  $A = r$ 
B)  $A = 2 r$ 
C)  $\mathrm { A } = 2 \mathrm { r } ^ { 2 }$ 
D)  $A = 4 r ^ { 2 }$

Question 17

Find the range of the function.
-$$f ( x ) = \frac { 5 } { 5 - x ^ { 2 } }$$

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 0 ) \cup [ 1 , \infty )$ 
D)  $( - \infty , 0 ) \cup [ 5 , \infty )$ 
A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 0 ) \cup [ 1 , \infty )$ 
D)  $( - \infty , 0 ) \cup [ 5 , \infty )$

Question 18

Find the (x,y) pair for the value of the parameter.
-$x = 6 t$ and $y = t ^ { 2 } - 9$ for $t = 3$

Accepted Answer

A)  $( 9,3 )$ 
B)  $( 18,9 )$ 
C)  $( 0,9 )$ 
D)  $( 18,0 )$ 
A)  $( 9,3 )$ 
B)  $( 18,9 )$ 
C)  $( 0,9 )$ 
D)  $( 18,0 )$

Question 19

Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = \sqrt { x + 6 } ; g ( x ) = \cos x$$
Find $f - g$.

Accepted Answer

A)  $\sqrt { x + 6 } + \cos x$; domain: $[ - 6 , \infty )$ 
B)  $\frac { \cos x } { \sqrt { x + 6 } } ;$ domain: $[ - 6 , \infty )$ 
C)  $( \cos x ) ( \sqrt { x + 6 } )$; domain: $[ - 6 , \infty )$ 
D)  $\sqrt { x + 6 } - \cos x$; domain: $[ - 6 , \infty )$ 
A)  $\sqrt { x + 6 } + \cos x$; domain: $[ - 6 , \infty )$ 
B)  $\frac { \cos x } { \sqrt { x + 6 } } ;$ domain: $[ - 6 , \infty )$ 
C)  $( \cos x ) ( \sqrt { x + 6 } )$; domain: $[ - 6 , \infty )$ 
D)  $\sqrt { x + 6 } - \cos x$; domain: $[ - 6 , \infty )$

Question 20

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Let $\mathrm { f } ( \mathrm { x } )$ compute the cost of a rental car after $x$ days of use at $\$ 28$ per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Accepted Answer

A)  The number of days rented for 28 dollars 
B)  The cost of rental for 28 days 
C)  The number of days rented for $x$ dollars 
D)  The cost of rental for $x$ days 
A)  The number of days rented for 28 dollars 
B)  The cost of rental for 28 days 
C)  The number of days rented for $x$ dollars 
D)  The cost of rental for $x$ days

Solve the problem. -Estimate graphically the local maximum and local minimum of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } - 3 x$ .

Match the numerical model to the corresponding model. - x 0 3 8 15 24 35 y 1 2 3 4 5 6

Fill in the blanks to complete the statement. -The graph of $y = - 5 x ^ { 3 } + 2$ can be obtained from the graph of $y = x ^ { 3 }$ by vertically stretching by a factor of ? reflecting across the $?$ -axis, and shifting vertically $?$ units in the $?$ direction.

Match the equation with the appropriate graph. - $f ( x ) = \frac { 18 } { x ^ { 2 } - 9 }$

Match the numerical model to the corresponding model. -

Match the function with the graph. -

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt { 0.1 x }$

Determine whether the formula determines y as a function of x. - $y = 15$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = - \sqrt { x + 4 }$

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

Find the inverse of the function. - $f ( x ) = \sqrt { 2 x + 1 }$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = 4 x + 8 , g ( x ) = 4 x ^ { 2 }$ Find $( f + g ) ( x )$ .

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions. -Graph f $+ g$ .

Solve the problem. -The following data set gives the average home value, in dollars, for a city at 5 -year intervals. Determine where $f$ is increasing or decreasing.

Write the specified quantity as a function of the specified variable. -A square is inscribed in a circle. Write the area of the square as a function of the radius.

Find the range of the function. - $f ( x ) = \frac { 5 } { 5 - x ^ { 2 } }$

Find the (x,y) pair for the value of the parameter. - $x = 6 t$ and $y = t ^ { 2 } - 9$ for $t = 3$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = \sqrt { x + 6 } ; g ( x ) = \cos x$ Find $f - g$ .

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Let $\mathrm { f } ( \mathrm { x } )$ compute the cost of a rental car after $x$ days of use at $\$ 28$ per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

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

Solve the problem. -Estimate graphically the local maximum and local minimum of f(x)=13x3+x2−3xf ( x ) = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } - 3 xf(x)=31​x3+x2−3x .

Match the numerical model to the corresponding model. - x 0 3 8 15 24 35 y 1 2 3 4 5 6

Fill in the blanks to complete the statement. -The graph of y=−5x3+2y = - 5 x ^ { 3 } + 2y=−5x3+2 can be obtained from the graph of y=x3y = x ^ { 3 }y=x3 by vertically stretching by a factor of ? reflecting across the ??? -axis, and shifting vertically ??? units in the ??? direction.

Match the equation with the appropriate graph. - f(x)=18x2−9f ( x ) = \frac { 18 } { x ^ { 2 } - 9 }f(x)=x2−918​

Match the numerical model to the corresponding model. -

Match the function with the graph. -

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)=0.1xg ( x ) = \sqrt { 0.1 x }g(x)=0.1x​

Determine whether the formula determines y as a function of x. - y=15y = 15y=15

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)=−x+4g ( x ) = - \sqrt { x + 4 }g(x)=−x+4​

Identify which of the twelve basic functions listed below fit the description given. -The two functions that have end behavior lim⁡x→∞f(x)=+∞\lim _ { x \rightarrow \infty } f ( x ) = + \inftylimx→∞​f(x)=+∞

Find the inverse of the function. - f(x)=2x+1f ( x ) = \sqrt { 2 x + 1 }f(x)=2x+1​

Perform the requested operation or operations. Find the domain of each. - f(x)=4x+8,g(x)=4x2f ( x ) = 4 x + 8 , g ( x ) = 4 x ^ { 2 }f(x)=4x+8,g(x)=4x2 Find (f+g)(x)( f + g ) ( x )(f+g)(x) .

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions. -Graph f +g+ g+g .

Solve the problem. -The following data set gives the average home value, in dollars, for a city at 5 -year intervals. Determine where fff is increasing or decreasing.

Write the specified quantity as a function of the specified variable. -A square is inscribed in a circle. Write the area of the square as a function of the radius.

Find the range of the function. - f(x)=55−x2f ( x ) = \frac { 5 } { 5 - x ^ { 2 } }f(x)=5−x25​

Find the (x,y) pair for the value of the parameter. - x=6tx = 6 tx=6t and y=t2−9y = t ^ { 2 } - 9y=t2−9 for t=3t = 3t=3

Perform the requested operation or operations. Find the domain of each. - f(x)=x+6;g(x)=cos⁡xf ( x ) = \sqrt { x + 6 } ; g ( x ) = \cos xf(x)=x+6​;g(x)=cosx Find f−gf - gf−g .

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

Solve the problem. -Estimate graphically the local maximum and local minimum of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } - 3 x$ .

Fill in the blanks to complete the statement. -The graph of $y = - 5 x ^ { 3 } + 2$ can be obtained from the graph of $y = x ^ { 3 }$ by vertically stretching by a factor of ? reflecting across the $?$ -axis, and shifting vertically $?$ units in the $?$ direction.

Match the equation with the appropriate graph. - $f ( x ) = \frac { 18 } { x ^ { 2 } - 9 }$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt { 0.1 x }$

Determine whether the formula determines y as a function of x. - $y = 15$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x }$ and $g ( x ) = - \sqrt { x + 4 }$

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

Find the inverse of the function. - $f ( x ) = \sqrt { 2 x + 1 }$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = 4 x + 8 , g ( x ) = 4 x ^ { 2 }$ Find $( f + g ) ( x )$ .

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions. -Graph f $+ g$ .

Solve the problem. -The following data set gives the average home value, in dollars, for a city at 5 -year intervals. Determine where $f$ is increasing or decreasing.

Find the range of the function. - $f ( x ) = \frac { 5 } { 5 - x ^ { 2 } }$

Find the (x,y) pair for the value of the parameter. - $x = 6 t$ and $y = t ^ { 2 } - 9$ for $t = 3$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = \sqrt { x + 6 } ; g ( x ) = \cos x$ Find $f - g$ .