Question 1

A ball thrown vertically into the air has its height above ground given by   , where t is in seconds and s is in feet. Find the maximum height of the ball. ​

Accepted Answer

A) 242 feet 
B) 121 feet 
C) 8 feet 
D) 16 feet 
E) 229 feet 
A) 242 feet 
B) 121 feet 
C) 8 feet 
D) 16 feet 
E) 229 feet

Question 2

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 3

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 4

If a firm has the following cost and revenue functions, find the break-even points. ​   ​

Accepted Answer

A) Break-even values are at  
And  
Units. 
B) Break-even values are at  
And  
Units. 
C) Break-even values are at  
And  
Units. 
D) Break-even values are at  
And  
Units. 
E) Break-even values are at  
And  
Units. 
A) Break-even values are at  
And  
Units. 
B) Break-even values are at  
And  
Units. 
C) Break-even values are at  
And  
Units. 
D) Break-even values are at  
And  
Units. 
E) Break-even values are at  
And  
Units.

Question 5

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

Accepted Answer

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

Question 6

If total costs are   and total revenues are   , find the break-even points. ​

Accepted Answer

A) Break-even values are at  
And  
Units. 
B) Break-even values are at  
And  
Units. 
C) Break-even values are at  
And  
Units. 
D) Break-even values are at  
And  
Units. 
E) Break-even values are at  
And  
Units. 
A) Break-even values are at  
And  
Units. 
B) Break-even values are at  
And  
Units. 
C) Break-even values are at  
And  
Units. 
D) Break-even values are at  
And  
Units. 
E) Break-even values are at  
And  
Units.

Question 7

The monthly charge for water in a small town is given by   , where x is water usage in hundreds of gallons and f (x) is cost in dollars. Find the monthly charge for 1900 gallons and for 2600 gallons. Round your answers to the nearest cent. ​

Accepted Answer

A) charge for 1900 gallons is $36.00 charge for 2600 gallons is $38.40 
B) charge for 1900 gallons is $788.00 charge for 2600 gallons is $1068.00 
C) charge for 1900 gallons is $36.00 charge for 2600 gallons is $46.40 
D) charge for 1900 gallons is $38.40 charge for 2600 gallons is $46.40 
E) charge for 1900 gallons is $36.00 charge for 2600 gallons is $74.40 
A) charge for 1900 gallons is $36.00 charge for 2600 gallons is $38.40 
B) charge for 1900 gallons is $788.00 charge for 2600 gallons is $1068.00 
C) charge for 1900 gallons is $36.00 charge for 2600 gallons is $46.40 
D) charge for 1900 gallons is $38.40 charge for 2600 gallons is $46.40 
E) charge for 1900 gallons is $36.00 charge for 2600 gallons is $74.40

Question 8

Find the zeros, if any exist. Round your answers to two decimal places. ​   ​

Accepted Answer

A) zeros at -2.17 and -7.83 
B) zeros at 0 and 10.00 
C) zeros at 11.00 and -21.00 
D) no zeros 
E) zeros at 0 and 27.00 
A) zeros at -2.17 and -7.83 
B) zeros at 0 and 10.00 
C) zeros at 11.00 and -21.00 
D) no zeros 
E) zeros at 0 and 27.00

Question 9

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

Accepted Answer

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

Question 10

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 11

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 12

If the supply and demand functions for a commodity are given by   and   , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places. ​

Accepted Answer

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

Question 13

Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places. ​   ​

Accepted Answer

A) optimal value of x: 0, optimal value: 1.00 
B) optimal value of x: -1.13, optimal value: 0.75 
C) optimal value of x: 1.50, optimal value: -1.50 
D) optimal value of x: -0.75, optimal value: -1.13 
E) optimal value of x: 0.75, optimal value: -1.13 
A) optimal value of x: 0, optimal value: 1.00 
B) optimal value of x: -1.13, optimal value: 0.75 
C) optimal value of x: 1.50, optimal value: -1.50 
D) optimal value of x: -0.75, optimal value: -1.13 
E) optimal value of x: 0.75, optimal value: -1.13

Question 14

The profit function for a certain commodity is   . Find the level of production that yields maximum profit, and find the maximum profit. ​

Accepted Answer

A) Production levels of 120 yields a maximum profit of $1,100. 
B) Production levels of 120 yields a maximum profit of $2,500. 
C) Production levels of 60 yields a maximum profit of $6,040. 
D) Production levels of 60 yields a maximum profit of $3,600. 
E) Production levels of 60 yields a maximum profit of $2,500. 
A) Production levels of 120 yields a maximum profit of $1,100. 
B) Production levels of 120 yields a maximum profit of $2,500. 
C) Production levels of 60 yields a maximum profit of $6,040. 
D) Production levels of 60 yields a maximum profit of $3,600. 
E) Production levels of 60 yields a maximum profit of $2,500.

Question 15

An equation that models the number of users of the Internet is   million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users? ​

Accepted Answer

A) 2004 
B) 2021 
C) 2014 
D) 2007 
E) 2005 
A) 2004 
B) 2021 
C) 2014 
D) 2007 
E) 2005

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

A shipping company's charges for delivery of a package is a function of the package's weight. The following table describes the company's shipping rates. ​   ​
Convert this table to a piecewise defined function that represents shipping costs for packages weighing between 0 and 4 pounds using x as the weight in pounds and C as the cost in dollars. Find the postage for a 0.75-pound package. Round your answer to the nearest cent.

Accepted Answer

A)   
Cost for a 0.75 lb package: $0.45
​ 
B)   
Cost for a 0.75 lb package: $0.23
​ 
C)   
Cost for a 0.75 lb package: $1.09
​ 
D)   
Cost for a 0.75 lb package: $0.45
​ 
E)   
Cost for a 0.75 lb package: $0.45 
A)   
Cost for a 0.75 lb package: $0.45
​ 
B)   
Cost for a 0.75 lb package: $0.23
​ 
C)   
Cost for a 0.75 lb package: $1.09
​ 
D)   
Cost for a 0.75 lb package: $0.45
​ 
E)   
Cost for a 0.75 lb package: $0.45

Question 18

The supply function for a product is   , while the demand function for the same product is   . Find the market equilibrium point E(q, p). Round your final answer to two decimal places. ​

Accepted Answer

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

Question 19

If the supply and demand functions for a commodity are given by   and   , respectively, find the price that will result in market equilibrium. ​

Accepted Answer

A) 41 
B) 150 
C) 33 
D) 31 
E) 25 
A) 41 
B) 150 
C) 33 
D) 31 
E) 25

Question 20

The table gives the median household income (in 2005 year) for two cities in various years. Let x represent the median household income for citizens of city A and y represent the corresponding median household income for citizens of city B. Find a linear model that expresses the median household income for citizens in city B as a function of the median household income for citizens of city B. Interpret the slope of the linear model. Round numerical values in your answer to three decimal places.

Accepted Answer

A)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
B)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
C)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
D)   
Slope: median household income is growing faster for city A than it is for city B. 
E)   
Slope: median household income is growing slower for city A than it is for city B. 
A)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
B)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
C)   
Slope: median household income is growing at the same rate for city A as it is for city B. 
D)   
Slope: median household income is growing faster for city A than it is for city B. 
E)   
Slope: median household income is growing slower for city A than it is for city B.

A ball thrown vertically into the air has its height above ground given by , where t is in seconds and s is in feet. Find the maximum height of the ball.

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

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.

If a firm has the following cost and revenue functions, find the break-even points.

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

If total costs are and total revenues are , find the break-even points.

The monthly charge for water in a small town is given by , where x is water usage in hundreds of gallons and f (x) is cost in dollars. Find the monthly charge for 1900 gallons and for 2600 gallons. Round your answers to the nearest cent.

Find the zeros, if any exist. Round your answers to two decimal places.

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

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

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

If the supply and demand functions for a commodity are given by and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places.

Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places.

The profit function for a certain commodity is . Find the level of production that yields maximum profit, and find the maximum profit.

An equation that models the number of users of the Internet is million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users?

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

The supply function for a product is , while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places.

If the supply and demand functions for a commodity are given by and , respectively, find the price that will result in market equilibrium.

Algebraic Concepts

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 3: Quadratic and Other Special Functions

A ball thrown vertically into the air has its height above ground given by , where t is in seconds and s is in feet. Find the maximum height of the ball. ​

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

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. ​ ​

If a firm has the following cost and revenue functions, find the break-even points. ​ ​

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

If total costs are and total revenues are , find the break-even points. ​

The monthly charge for water in a small town is given by , where x is water usage in hundreds of gallons and f (x) is cost in dollars. Find the monthly charge for 1900 gallons and for 2600 gallons. Round your answers to the nearest cent. ​

Find the zeros, if any exist. Round your answers to two decimal places. ​ ​

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

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

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

If the supply and demand functions for a commodity are given by and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places. ​

Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places. ​ ​

The profit function for a certain commodity is . Find the level of production that yields maximum profit, and find the maximum profit. ​

An equation that models the number of users of the Internet is million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users? ​

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

The supply function for a product is , while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places. ​

If the supply and demand functions for a commodity are given by and , respectively, find the price that will result in market equilibrium. ​

Algebraic Concepts

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

A ball thrown vertically into the air has its height above ground given by , where t is in seconds and s is in feet. Find the maximum height of the ball.

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

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.

If a firm has the following cost and revenue functions, find the break-even points.

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

If total costs are and total revenues are , find the break-even points.

The monthly charge for water in a small town is given by , where x is water usage in hundreds of gallons and f (x) is cost in dollars. Find the monthly charge for 1900 gallons and for 2600 gallons. Round your answers to the nearest cent.

Find the zeros, if any exist. Round your answers to two decimal places.

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

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

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

If the supply and demand functions for a commodity are given by and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places.

Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places.

The profit function for a certain commodity is . Find the level of production that yields maximum profit, and find the maximum profit.

An equation that models the number of users of the Internet is million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users?

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

The supply function for a product is , while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places.

If the supply and demand functions for a commodity are given by and , respectively, find the price that will result in market equilibrium.