Question 1

Graph the quadratic function that models the data given in the table below. ​

Accepted Answer

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

Question 2

Solve   for the function   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  no real solutions 
A)    
B)    
C)    
D)    
E)  no real solutions

Question 3

Solve the equation   by using a graphing utility. Round your answers to two decimal places. ​

Accepted Answer

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

Question 4

The daily profit from the sale of a product is given by   dollars. What level of production maximizes profit? ​

Accepted Answer

A)  production level of 100 units 
B)  production level of 10 units 
C)  production level of 5 units 
D)  production level of 50 units 
E)  production level of 95 units 
A)  production level of 100 units 
B)  production level of 10 units 
C)  production level of 5 units 
D)  production level of 50 units 
E)  production level of 95 units

Question 5

Find the equation of the quartic function that is the best fit for the given data. Round your final values to two decimal places. ​
 
​

Accepted Answer

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

Question 6

The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend? ​

Accepted Answer

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

Question 7

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points. ​   ​

Accepted Answer

A)  piecewise function
Turning points:   and   
B)  polynomial function
Turning points:   and   
C)  rational function
Turning points:   
D)  polynomial function
Turning points:   
E)  piecewise function
Turning points:   
A)  piecewise function
Turning points:   and   
B)  polynomial function
Turning points:   and   
C)  rational function
Turning points:   
D)  polynomial function
Turning points:   
E)  piecewise function
Turning points:

Question 8

Find the rational function whose graph is given. ​   ​

Accepted Answer

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

Question 9

The total costs for a company are given by   , and the total revenues are given by   . Find the break-even points. ​

Accepted Answer

A)  Break-even values are at x = 35 and x = 70 units. 
B)  Break-even values are at x = inf units. 
C)  Break-even values are at x = -inf units. 
D)  Break-even values are at x = 17.5 and x = 35 units. 
E)  Break-even values are at x = 70 units. 
A)  Break-even values are at x = 35 and x = 70 units. 
B)  Break-even values are at x = inf units. 
C)  Break-even values are at x = -inf units. 
D)  Break-even values are at x = 17.5 and x = 35 units. 
E)  Break-even values are at x = 70 units.

Question 10

Find the exact real solutions of the equation   , if they exist. ​

Accepted Answer

A)    and   
B)    and   
C)    and   
D)    and   
E)  Real solutions do not exist. 
A)    and   
B)    and   
C)    and   
D)    and   
E)  Real solutions do not exist.

Question 11

How is the graph of   shifted to obtain the graph of the function   ? ​

Accepted Answer

A)  shifted 12 units to the left and 13 units up 
B)  shifted 12 units to the right and 13 units down 
C)  shifted 144 units to the left and 13 units up 
D)  shifted 24 units to the right and 13 units down 
E)  shifted 12 units to the right and 13 units up 
A)  shifted 12 units to the left and 13 units up 
B)  shifted 12 units to the right and 13 units down 
C)  shifted 144 units to the left and 13 units up 
D)  shifted 24 units to the right and 13 units down 
E)  shifted 12 units to the right and 13 units up

Question 12

Assume that sales revenues for Continental Divide Mining can be described by   , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs. ​

Accepted Answer

A)  Maximum revenue occurred during 1998. 
B)  Maximum revenue occurred during 1992. 
C)  Maximum revenue occurred during 1997. 
D)  Maximum revenue occurred during 2003. 
E)  Maximum revenue occurred during 1991. 
A)  Maximum revenue occurred during 1998. 
B)  Maximum revenue occurred during 1992. 
C)  Maximum revenue occurred during 1997. 
D)  Maximum revenue occurred during 2003. 
E)  Maximum revenue occurred during 1991.

Question 13

Graph the linear function that models the data given in the table below. ​

Accepted Answer

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

Question 14

Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. ​   ​

Accepted Answer

A)  vertex:   , a minimum point 
B)  vertex:   , a maximum point 
C)  vertex:   , a minimum point 
D)  vertex:   , a maximum point 
E)  vertex:   , a maximum point 
A)  vertex:   , a minimum point 
B)  vertex:   , a maximum point 
C)  vertex:   , a minimum point 
D)  vertex:   , a maximum point 
E)  vertex:   , a maximum point

Question 15

The demand function for a product is given by   , where x is the number of units and p is the price in dollars. The graph of this demand function for   , with x on the horizontal axis is given below. Does the demand function ever reach 0?
​

Accepted Answer

A) True 
 B)False

Question 16

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. ​
​   ​

Accepted Answer

A)  linear 
B)  power 
C)  quadratic 
D)  cubic 
E)  quartic 
A)  linear 
B)  power 
C)  quadratic 
D)  cubic 
E)  quartic

Question 17

Suppose the following table gives the U.S. population, in millions, for selected years, with projections to 2050. Find a linear model that approximately fits the data, with x equal to the number of years past 1960. Round numerical values in your answer to three decimal places. Depending on the technology you use, your answer may be slightly different than the correct answer shown.​ ​
 
​

Accepted Answer

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

Question 18

Find the equation of the cubic function that is the best fit for the given data. Round your final values to two decimal places. ​

Accepted Answer

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

Question 19

Find the vertex of the graph of the equation   . Round your answer to two decimal places. ​

Accepted Answer

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

Question 20

Use a graphing utility to approximate the solutions to   . Round your answers to two decimal places. ​   ​

Accepted Answer

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

Graph the quadratic function that models the data given in the table below.

Solve for the function .

Solve the equation by using a graphing utility. Round your answers to two decimal places.

The daily profit from the sale of a product is given by dollars. What level of production maximizes profit?

Find the equation of the quartic function that is the best fit for the given data. Round your final values to two decimal places.

The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend?

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points.

Find the rational function whose graph is given.

The total costs for a company are given by , and the total revenues are given by . Find the break-even points.

Find the exact real solutions of the equation , if they exist.

How is the graph of shifted to obtain the graph of the function ?

Assume that sales revenues for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs.

Graph the linear function that models the data given in the table below.

Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point.

The demand function for a product is given by , where x is the number of units and p is the price in dollars. The graph of this demand function for , with x on the horizontal axis is given below. Does the demand function ever reach 0?

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function.

Find the equation of the cubic function that is the best fit for the given data. Round your final values to two decimal places.

Find the vertex of the graph of the equation . Round your answer to two decimal places.

Use a graphing utility to approximate the solutions to . Round your answers to two decimal places.

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 2: Quadratic and Other Special Functions

Graph the quadratic function that models the data given in the table below. ​

Solve for the function . ​

Solve the equation by using a graphing utility. Round your answers to two decimal places. ​

The daily profit from the sale of a product is given by dollars. What level of production maximizes profit? ​

Find the equation of the quartic function that is the best fit for the given data. Round your final values to two decimal places. ​ ​

The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend? ​

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points. ​ ​

Find the rational function whose graph is given. ​ ​

The total costs for a company are given by , and the total revenues are given by . Find the break-even points. ​

Find the exact real solutions of the equation , if they exist. ​

How is the graph of shifted to obtain the graph of the function ? ​

Assume that sales revenues for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs. ​

Graph the linear function that models the data given in the table below. ​

Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. ​ ​

The demand function for a product is given by , where x is the number of units and p is the price in dollars. The graph of this demand function for , with x on the horizontal axis is given below. Does the demand function ever reach 0? ​

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. ​ ​ ​

Find the equation of the cubic function that is the best fit for the given data. Round your final values to two decimal places. ​

Find the vertex of the graph of the equation . Round your answer to two decimal places. ​

Use a graphing utility to approximate the solutions to . Round your answers to two decimal places. ​ ​

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Graph the quadratic function that models the data given in the table below.

Solve for the function .

Solve the equation by using a graphing utility. Round your answers to two decimal places.

The daily profit from the sale of a product is given by dollars. What level of production maximizes profit?

Find the equation of the quartic function that is the best fit for the given data. Round your final values to two decimal places.

The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend?

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points.

Find the rational function whose graph is given.

The total costs for a company are given by , and the total revenues are given by . Find the break-even points.

Find the exact real solutions of the equation , if they exist.

How is the graph of shifted to obtain the graph of the function ?

Assume that sales revenues for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs.

Graph the linear function that models the data given in the table below.

Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point.

The demand function for a product is given by , where x is the number of units and p is the price in dollars. The graph of this demand function for , with x on the horizontal axis is given below. Does the demand function ever reach 0?

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function.

Find the equation of the cubic function that is the best fit for the given data. Round your final values to two decimal places.

Find the vertex of the graph of the equation . Round your answer to two decimal places.

Use a graphing utility to approximate the solutions to . Round your answers to two decimal places.