Question 1

For   and   , find   . ​

Accepted Answer

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

Question 2

Use a graphing utility with the standard viewing window   and   to graph the function. Choose the correct graph below. ​​   ​

Accepted Answer

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

Question 3

The percent of the U.S. population with Internet service can be described by   , where x is the number of years past 1995. What interpretation could be given to the y-intercept of this equation? ​

Accepted Answer

A)  In 1995, 13.13% more of the U.S. population had Internet access than in the previous year. 
B)  In 1995, the number of people in the U.S. with Internet access increased at a rate of 13.13% per year. 
C)  At present, the number of people in the U.S. with Internet access is increasing at a rate of 13.13% per year. 
D)  In 1995, 13.13% of the U.S. population had Internet access. 
E)  At present, 13.13% of the U.S. population has Internet access. 
A)  In 1995, 13.13% more of the U.S. population had Internet access than in the previous year. 
B)  In 1995, the number of people in the U.S. with Internet access increased at a rate of 13.13% per year. 
C)  At present, the number of people in the U.S. with Internet access is increasing at a rate of 13.13% per year. 
D)  In 1995, 13.13% of the U.S. population had Internet access. 
E)  At present, 13.13% of the U.S. population has Internet access.

Question 4

Suppose the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by   . Because p is the percent particulate pollution, we know   . Use the restriction on p and experiment with a C-range to obtain an accurate graph of the equation. Determine the p-intercept and explain its meaning. ​

Accepted Answer

A)  The p-intercept is (0,0) , meaning that it costs nothing to remove all of the particulate pollution. 
B)  The p-intercept is (0,72), meaning that there is a cost of $72 before the removal of the particulate pollution begins. 
C)  There is no p-intercept, which means that it is impossible to remove all of the particulate pollution. 
D)  The p-intercept is (0,0), meaning that it costs nothing to remove none of the particulate pollution. 
E)  The p-intercept is (0, -72), meaning that there is a negative cost of $72 before the removal of the particulate pollution begins. 
A)  The p-intercept is (0,0) , meaning that it costs nothing to remove all of the particulate pollution. 
B)  The p-intercept is (0,72), meaning that there is a cost of $72 before the removal of the particulate pollution begins. 
C)  There is no p-intercept, which means that it is impossible to remove all of the particulate pollution. 
D)  The p-intercept is (0,0), meaning that it costs nothing to remove none of the particulate pollution. 
E)  The p-intercept is (0, -72), meaning that there is a negative cost of $72 before the removal of the particulate pollution begins.

Question 5

Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression   . ​

Accepted Answer

A)  painting the door and then sanding 
B)  painting the door twice 
C)  sanding the door twice 
D)  sanding the door and then painting 
A)  painting the door and then sanding 
B)  painting the door twice 
C)  sanding the door twice 
D)  sanding the door and then painting

Question 6

Find the domain and range of the function below. ​   ​

Accepted Answer

A)  domain: real numbers  
Range: real numbers   
B)  domain: real numbers  
Range: real numbers   
C)  domain: all reals
Range: real numbers   
D)  domain: real numbers  
Range: real numbers   
E)  domain: all reals
Range: real numbers   
A)  domain: real numbers  
Range: real numbers   
B)  domain: real numbers  
Range: real numbers   
C)  domain: all reals
Range: real numbers   
D)  domain: real numbers  
Range: real numbers   
E)  domain: all reals
Range: real numbers

Question 7

Use the left-to-right elimination method to solve the system. ​   ​

Accepted Answer

A)  solution:   
B)  solution:   
C)  solution:   
D)  solution:   
E)  solution:   
A)  solution:   
B)  solution:   
C)  solution:   
D)  solution:   
E)  solution:

Question 8

Find the intercepts of the following function. ​   ​

Accepted Answer

A)  x-intercept: -8.5
Y-intercept: 17 
B)  x-intercept: 17
Y-intercept: 34 
C)  x-intercept: -34
Y-intercept: 8.5 
D)  x-intercept: -17
Y-intercept: 2 
E)  x-intercept: 8.5
Y-intercept: -17 
A)  x-intercept: -8.5
Y-intercept: 17 
B)  x-intercept: 17
Y-intercept: 34 
C)  x-intercept: -34
Y-intercept: 8.5 
D)  x-intercept: -17
Y-intercept: 2 
E)  x-intercept: 8.5
Y-intercept: -17

Question 9

According to the U.S. Bureau of the Census, the relation between the average annual earnings of males and females with various levels of educational attainment can be modeled by the function F = 0.569M + 6.293 where M and F represent the average annual earnings (in thousands of dollars) of males and females, respectively. When the average annual earnings for males reach $70,000, what does the equation predict for the average annual earnings for females? Round your answer to the nearest dollar. ​

Accepted Answer

A)  $123,029 
B)  $39,830 
C)  $46,123 
D)  $42,681 
E)  $36,991 
A)  $123,029 
B)  $39,830 
C)  $46,123 
D)  $42,681 
E)  $36,991

Question 10

A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.25 per square foot and the material for the top costs $1.25 per square foot, express the total cost (in dollars) of material for the box as a function of x. ​

Accepted Answer

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

Question 11

The Millcreek watershed area was heavily strip-mined for coal during the late 1960s. Because of the resulting pollution, the streams cannot support fish. Suppose the cost C of obtaining stream water that contains p percent of the current pollution levels is given by   . Because p is the percent of current pollution levels,   . Use the restriction on p and determine a range for C so that an accurate graph can be obtained with a graphing utility. Describe what happens to the cost as p takes on positive values near 0. ​

Accepted Answer

A)  Near p = 0, the cost approaches $3,380. 
B)  Near p = 0, the cost grows without bound. 
C)  Near p = 0, the cost approaches $338,000. 
D)  Near p = 0, cost approaches $0. 
E)  Near p = 0, the cost becomes negative. 
A)  Near p = 0, the cost approaches $3,380. 
B)  Near p = 0, the cost grows without bound. 
C)  Near p = 0, the cost approaches $338,000. 
D)  Near p = 0, cost approaches $0. 
E)  Near p = 0, the cost becomes negative.

Question 12

Graph the function using a window that gives a complete graph. Does the figure below show the complete graph?
​   ​   ​

Accepted Answer

A) True 
 B)False

Question 13

Solve the system by elimination, or by any convenient method. ​
​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  There is no solution to the equations. 
A)    
B)    
C)    
D)    
E)  There is no solution to the equations.

Question 14

Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by   , where x is the number of years past 1975. What is the slope of the graph of this function? ​

Accepted Answer

A)  - 0.292 
B)  0.186 
C)  - 2.917 
D)  - 0.186 
E)  29.166 
A)  - 0.292 
B)  0.186 
C)  - 2.917 
D)  - 0.186 
E)  29.166

Question 15

Suppose that the total cost function for a radio is linear, that the marginal cost is $27, and that the total cost for 50 radios is $4,850. Write the equation of this cost function   . ​

Accepted Answer

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

Question 16

Suppose a mining company will supply 80,000 tons of ore per month if the price is $25 per ton but will supply only 60,000 tons per month if the price is $20 per ton. Assume the demand function is linear. Choose the correct equation for demand in the form p for price in terms of q for quantity. Round your coefficients to five decimal places. ​

Accepted Answer

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

Question 17

Use the left-to-right elimination method to solve the system. ​   ​

Accepted Answer

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

Question 18

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments? ​

Accepted Answer

A)  $11,700 
B)  $16,900 
C)  $57,500 
D)  $72,500 
E)  $113,100 
A)  $11,700 
B)  $16,900 
C)  $57,500 
D)  $72,500 
E)  $113,100

Question 19

Write the equation of the line through (2,4) that is parallel to

Accepted Answer

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

Question 20

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts? ​   ​

Accepted Answer

A)  x-min = -100 x-max = 300
Y-min = -10,000 y-max = 30,000 
B)  x-min = -100 x-max = 300
Y-min = -10,000 y-max = 50,000 
C)  x-min = -100 x-max = 500
Y-min = -10,000 y-max = 30,000 
D)  x-min = -100 x-max = 500
Y-min = -10,000 y-max = 50,000 
E)  ​x-min = 100 x-max = 300
Y-min = 10,000 y-max = 30,000 
A)  x-min = -100 x-max = 300
Y-min = -10,000 y-max = 30,000 
B)  x-min = -100 x-max = 300
Y-min = -10,000 y-max = 50,000 
C)  x-min = -100 x-max = 500
Y-min = -10,000 y-max = 30,000 
D)  x-min = -100 x-max = 500
Y-min = -10,000 y-max = 50,000 
E)  ​x-min = 100 x-max = 300
Y-min = 10,000 y-max = 30,000

For and , find .

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below.

The percent of the U.S. population with Internet service can be described by , where x is the number of years past 1995. What interpretation could be given to the y-intercept of this equation?

Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression .

Find the domain and range of the function below.

Use the left-to-right elimination method to solve the system.

Find the intercepts of the following function.

Graph the function using a window that gives a complete graph. Does the figure below show the complete graph?

Solve the system by elimination, or by any convenient method.

Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by , where x is the number of years past 1975. What is the slope of the graph of this function?

Suppose that the total cost function for a radio is linear, that the marginal cost is $27, and that the total cost for 50 radios is $4,850. Write the equation of this cost function .

Use the left-to-right elimination method to solve the system.

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments?

Write the equation of the line through (2,4) that is parallel to

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts?

Quadratic and Other Special 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 1: Linear Equations and Functions

For and , find . ​

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below. ​​ ​

The percent of the U.S. population with Internet service can be described by , where x is the number of years past 1995. What interpretation could be given to the y-intercept of this equation? ​

Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression . ​

Find the domain and range of the function below. ​ ​

Use the left-to-right elimination method to solve the system. ​ ​

Find the intercepts of the following function. ​ ​

Graph the function using a window that gives a complete graph. Does the figure below show the complete graph? ​ ​ ​

Solve the system by elimination, or by any convenient method. ​ ​ ​

Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by , where x is the number of years past 1975. What is the slope of the graph of this function? ​

Suppose that the total cost function for a radio is linear, that the marginal cost is $27, and that the total cost for 50 radios is $4,850. Write the equation of this cost function . ​

Use the left-to-right elimination method to solve the system. ​ ​

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments? ​

Write the equation of the line through (2,4) that is parallel to

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts? ​ ​

Quadratic and Other Special 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

For and , find .

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below.

The percent of the U.S. population with Internet service can be described by , where x is the number of years past 1995. What interpretation could be given to the y-intercept of this equation?

Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression .

Find the domain and range of the function below.

Use the left-to-right elimination method to solve the system.

Find the intercepts of the following function.

Graph the function using a window that gives a complete graph. Does the figure below show the complete graph?

Solve the system by elimination, or by any convenient method.

Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by , where x is the number of years past 1975. What is the slope of the graph of this function?

Suppose that the total cost function for a radio is linear, that the marginal cost is $27, and that the total cost for 50 radios is $4,850. Write the equation of this cost function .

Use the left-to-right elimination method to solve the system.

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments?

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts?