Question 1

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

Accepted Answer

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

Question 2

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)

Question 3

Sketch the graph of the function   . ​

Accepted Answer

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

Question 4

Suppose the IQ scores (rounded to the nearest 10) for a group of people are summarized in the table below. Find the quadratic function that best fits the data, using x as the IQ score and y as the number of people in the group with that IQ score. Use a graphing utility to estimate the IQ score of the maximum number of individuals according to the model. Round your final answer to 2 decimal places. ​

Accepted Answer

A)   
The model predicts that the maximum number of people have an IQ score of approximately 94. 
B)   
The model predicts that the maximum number of people have an IQ score of approximately 90. 
C)   
The model predicts that the maximum number of people have an IQ score of approximately 90. 
D)   
The model predicts that the maximum number of people have an IQ score of approximately 94. 
E)   
The model predicts that the maximum number of people have an IQ score of approximately 90. 
A)   
The model predicts that the maximum number of people have an IQ score of approximately 94. 
B)   
The model predicts that the maximum number of people have an IQ score of approximately 90. 
C)   
The model predicts that the maximum number of people have an IQ score of approximately 90. 
D)   
The model predicts that the maximum number of people have an IQ score of approximately 94. 
E)   
The model predicts that the maximum number of people have an IQ score of approximately 90.

Question 5

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 6

Find the vertex and then determine the range of the function. ​   ​

Accepted Answer

A) all values greater than or equal to 67 
B) all values less than or equal to 63 
C) all values greater than or equal to 10 
D) all values less than or equal to 85 
E) all values less than or equal to 67 
A) all values greater than or equal to 67 
B) all values less than or equal to 63 
C) all values greater than or equal to 10 
D) all values less than or equal to 85 
E) all values less than or equal to 67

Question 7

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

Accepted Answer

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

Question 8

Solve the equation   by factoring. ​

Accepted Answer

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

Question 9

Suppose a company has fixed costs of $27,000 and variable costs of   dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is   dollars per unit. Find the maximum revenue. Round your answer to the nearest cent. ​

Accepted Answer

A) Maximum revenue is $1,026.70. 
B) Maximum revenue is $27,000.00. 
C) Maximum revenue is $26,862.50. 
D) Maximum revenue is $677,343.75. 
E) Maximum revenue is $612.50. 
A) Maximum revenue is $1,026.70. 
B) Maximum revenue is $27,000.00. 
C) Maximum revenue is $26,862.50. 
D) Maximum revenue is $677,343.75. 
E) Maximum revenue is $612.50.

Question 10

The demand function for a product is given by   , where x is the number of units and p is the price in dollars. Graph this demand function for   , with x on the horizontal axis. ​

Accepted Answer

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

Question 11

The amount of money invested in a certain mutual funds, measured in millions of dollars, for the years 1995 to 1999 was found to be modeled by   million dollars, where x is the number of years past 1990. Will the graph of this function bend upward or will it bend downward? How much money is predicted to be in the fund in the year 2009? Round your answer to two decimal places. ​

Accepted Answer

A) the function's graph bends upward; the function predicts 134,947.08 million dollars in 2009 
B) the function's graph bends downward; the function predicts 134,947.08 million dollars in 2009 
C) the function's graph bends upward; the function predicts 68,279.14 million dollars in 2009 
D) the function's graph bends downward; the function predicts 1,611.20 million dollars in 2009 
E) the function's graph bends upward; the function predicts 1,611.20 million dollars in 2009 
A) the function's graph bends upward; the function predicts 134,947.08 million dollars in 2009 
B) the function's graph bends downward; the function predicts 134,947.08 million dollars in 2009 
C) the function's graph bends upward; the function predicts 68,279.14 million dollars in 2009 
D) the function's graph bends downward; the function predicts 1,611.20 million dollars in 2009 
E) the function's graph bends upward; the function predicts 1,611.20 million dollars in 2009

Question 12

Suppose that the percent of total personal income that is used to pay personal taxes is given by   , where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 20 percent. ​

Accepted Answer

A) 2015 
B) 2005 
C) 2004 
D) 2010 
E) 2050 
A) 2015 
B) 2005 
C) 2004 
D) 2010 
E) 2050

Question 13

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places. ​   ​​

Accepted Answer

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

Question 14

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 15

The daily profit from the sale of a product is given by   dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. ​

Accepted Answer

A) $5,423 
B) $16,685 
C) $11,013 
D) $137 
E) $271 
A) $5,423 
B) $16,685 
C) $11,013 
D) $137 
E) $271

Question 16

Given the profit function,   , and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places. ​

Accepted Answer

A) Break-even value is at  
Units. 
B) Break-even value is at  
Units. 
C) Break-even value is at  
Units. 
D) Break-even value is at  
Units. 
E) Break-even value is at  
Units. 
A) Break-even value is at  
Units. 
B) Break-even value is at  
Units. 
C) Break-even value is at  
Units. 
D) Break-even value is at  
Units. 
E) Break-even value is at  
Units.

Question 17

Sketch the first quadrant portions of the following functions and estimate the market equilibrium point. ​
Supply:   Demand:   ​

Accepted Answer

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

Question 18

Sketch the graph of the following function. ​

Accepted Answer

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

Question 19

The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by   . Find the value of s that will make   . ​

Accepted Answer

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

Question 20

The table gives the percent of the population of a certain city that was foreign born in the given year. Find a cubic function that best fits the data where x is the number of years after 1900 and y is equal to the percent. By trial and error, estimate the year the model predicts that the foreign-born population will be 100%. Round numerical values in your answer to three decimal places. ​   ​

Accepted Answer

A)   
Foreign born population will be 100% in 1965. 
B)   
Foreign born population will be 100% in 1975. 
C)   
Foreign born population will be 100% in 1975. 
D)   
Foreign born population will be 100% in 1965. 
E)   
Foreign born population will be 100% in 1985. 
A)   
Foreign born population will be 100% in 1965. 
B)   
Foreign born population will be 100% in 1975. 
C)   
Foreign born population will be 100% in 1975. 
D)   
Foreign born population will be 100% in 1965. 
E)   
Foreign born population will be 100% in 1985.

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

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

Sketch the graph of the function .

Find the vertex and then determine the range of the function.

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

Solve the equation by factoring.

Suppose a company has fixed costs of $27,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent.

The demand function for a product is given by , where x is the number of units and p is the price in dollars. Graph this demand function for , with x on the horizontal axis.

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places.

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

The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.

Given the profit function, , and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places.

Sketch the first quadrant portions of the following functions and estimate the market equilibrium point. Supply: Demand:

Sketch the graph of the following function.

The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by . Find the value of s that will make .

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

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

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

Sketch the graph of the function . ​

Find the vertex and then determine the range of the function. ​ ​

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

Solve the equation by factoring. ​

Suppose a company has fixed costs of $27,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent. ​

The demand function for a product is given by , where x is the number of units and p is the price in dollars. Graph this demand function for , with x on the horizontal axis. ​

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places. ​ ​​

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

The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. ​

Given the profit function, , and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places. ​

Sketch the first quadrant portions of the following functions and estimate the market equilibrium point. ​ Supply: Demand: ​

Sketch the graph of the following function. ​

The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by . Find the value of s that will make . ​

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

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

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

Sketch the graph of the function .

Find the vertex and then determine the range of the function.

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

Solve the equation by factoring.

Suppose a company has fixed costs of $27,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent.

The demand function for a product is given by , where x is the number of units and p is the price in dollars. Graph this demand function for , with x on the horizontal axis.

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places.

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

The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.

Given the profit function, , and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places.

Sketch the first quadrant portions of the following functions and estimate the market equilibrium point. Supply: Demand:

Sketch the graph of the following function.

The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by . Find the value of s that will make .