Question 1

If the profit from the sale of x units of a product is   , what level(s) of production will yield a profit of $1,600? ​

Accepted Answer

A) less 35 units of production. 
B) more than 50 units of production. 
C) 85 units of production. 
D) 15 units of production. 
E) 35 or 50 units of production. 
A) less 35 units of production. 
B) more than 50 units of production. 
C) 85 units of production. 
D) 15 units of production. 
E) 35 or 50 units of production.

Question 2

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. Round your answers to two decimal places. ​   ​

Accepted Answer

A) polynomial function turning points:  
And   
B) rational function turning points:  
And   
C) polynomial function turning points:  
,  
, and   
D) rational function turning points:  
,  
, and   
E) piecewise function turning points:  
And   
A) polynomial function turning points:  
And   
B) rational function turning points:  
And   
C) polynomial function turning points:  
,  
, and   
D) rational function turning points:  
,  
, and   
E) piecewise function turning points:  
And

Question 3

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is estimated by   . What is the domain of this function? What will it cost to remove 99.0% of the particulate pollution? Round your answer to the nearest cent.

Accepted Answer

A) domain:  
Cost: $737,550.00 
B) domain:  
Cost: $737,550.00 
C) domain: all p except p = 100 cost: $737,550.00 
D) domain:  
Cost: $74.49 
E) domain: all p except p = 100 cost: $74.49 
A) domain:  
Cost: $737,550.00 
B) domain:  
Cost: $737,550.00 
C) domain: all p except p = 100 cost: $737,550.00 
D) domain:  
Cost: $74.49 
E) domain: all p except p = 100 cost: $74.49

Question 4

Sketch the graph of the following function by using graphing calculator. ​   ​

Accepted Answer

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

Question 5

Sketch the graph of the function   . ​

Accepted Answer

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

Question 6

Solve the equation by using the quadratic formula. Give real solutions only. ​   ​

Accepted Answer

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

Question 7

Write the equation   in general form. ​

Accepted Answer

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

Question 8

The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation   where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 42 mph. Round your answer to the nearest integer. ​

Accepted Answer

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

Question 9

The table that follows gives the population of a city. Find the power function that best fits the data, with x equal to the number of years past 1950. According to the model, will the city's population be greater than 1,400 by the year 2010? Round your final answer to three decimal places.

Accepted Answer

A)   
The model predicts that the population will not be greater than 1,400. 
B)   
The model predicts that the population will not be greater than 1,400. 
C)   
The model predicts that the population will be greater than 1,400. 
D)   
The model predicts that the population will be greater than 1,400. 
E)   
The model predicts that the population will not be greater than 1,400. 
A)   
The model predicts that the population will not be greater than 1,400. 
B)   
The model predicts that the population will not be greater than 1,400. 
C)   
The model predicts that the population will be greater than 1,400. 
D)   
The model predicts that the population will be greater than 1,400. 
E)   
The model predicts that the population will not be greater than 1,400.

Question 10

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 2001. 
B) Maximum revenue occurred during 1992. 
C) Maximum revenue occurred during 2000. 
D) Maximum revenue occurred during 2009. 
E) Maximum revenue occurred during 1991. 
A) Maximum revenue occurred during 2001. 
B) Maximum revenue occurred during 1992. 
C) Maximum revenue occurred during 2000. 
D) Maximum revenue occurred during 2009. 
E) Maximum revenue occurred during 1991.

Question 11

Factor the function   . ​

Accepted Answer

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

Question 12

The sensitivity S to a drug is related to the dosage size by   , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. ​

Accepted Answer

A)   
Milliliters,  
Milliliters 
B)   
Milliliters,  
Milliliters 
C)   
Milliliters,  
Milliliters 
D)   
Milliliters,  
Milliliters 
E)   
Milliliters 
A)   
Milliliters,  
Milliliters 
B)   
Milliliters,  
Milliliters 
C)   
Milliliters,  
Milliliters 
D)   
Milliliters,  
Milliliters 
E)   
Milliliters

Question 13

Assume that costs and expenses for Continental Divide Mining can be described by   and the sales revenue can be described by   , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs. ​

Accepted Answer

A) 2014 
B) 1993 
C) 2003 
D) 2004 
E) 1994 
A) 2014 
B) 1993 
C) 2003 
D) 2004 
E) 1994

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

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

Accepted Answer

A) shifted 3 units to the left and 6 units up 
B) shifted 3 units to the right and 6 units down 
C) shifted 9 units to the left and 6 units up 
D) shifted 6 units to the right and 6 units down 
E) shifted 3 units to the right and 6 units up 
A) shifted 3 units to the left and 6 units up 
B) shifted 3 units to the right and 6 units down 
C) shifted 9 units to the left and 6 units up 
D) shifted 6 units to the right and 6 units down 
E) shifted 3 units to the right and 6 units up

Question 16

Sketch the graph of the function   . ​

Accepted Answer

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

Question 17

Solve the equation below using quadratic methods. ​   ​

Accepted Answer

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

Question 18

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) Yes 
B) No 
A) Yes 
B) No

Question 19

The given graph shows the cost C, in thousands of dollars, of a production run for a product when x machines are used. Estimate the company's fixed cost of production to the nearest thousand dollars, and determine the number of machines that will result in maximum cost for the company. ​   ​

Accepted Answer

A) fixed production cost: $6,000 maximum cost when 4 machines used 
B) fixed production cost: $9,000 maximum cost when 4 machines used 
C) fixed production cost: $5,000 maximum cost when 4 machines used 
D) fixed production cost: $6,000 maximum cost when 6 machines used 
E) fixed production cost: $5,000 maximum cost when 6 machines used 
A) fixed production cost: $6,000 maximum cost when 4 machines used 
B) fixed production cost: $9,000 maximum cost when 4 machines used 
C) fixed production cost: $5,000 maximum cost when 4 machines used 
D) fixed production cost: $6,000 maximum cost when 6 machines used 
E) fixed production cost: $5,000 maximum cost when 6 machines used

Question 20

Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by   and   . ​

Accepted Answer

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

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,600?

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. Round your answers to two decimal places.

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is estimated by . What is the domain of this function? What will it cost to remove 99.0% of the particulate pollution? Round your answer to the nearest cent.

Sketch the graph of the following function by using graphing calculator.

Sketch the graph of the function .

Solve the equation by using the quadratic formula. Give real solutions only.

Write the equation in general form.

The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 42 mph. Round your answer to the nearest integer.

The table that follows gives the population of a city. Find the power function that best fits the data, with x equal to the number of years past 1950. According to the model, will the city's population be greater than 1,400 by the year 2010? Round your final answer to three decimal places.

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.

Factor the function .

The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity.

Assume that costs and expenses for Continental Divide Mining can be described by and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs.

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

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

Sketch the graph of the function .

Solve the equation below using quadratic methods.

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?

The given graph shows the cost C, in thousands of dollars, of a production run for a product when x machines are used. Estimate the company's fixed cost of production to the nearest thousand dollars, and determine the number of machines that will result in maximum cost for the company.

Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by and .

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

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,600? ​

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. Round your answers to two decimal places. ​ ​

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is estimated by . What is the domain of this function? What will it cost to remove 99.0% of the particulate pollution? Round your answer to the nearest cent.

Sketch the graph of the following function by using graphing calculator. ​ ​

Sketch the graph of the function . ​

Solve the equation by using the quadratic formula. Give real solutions only. ​ ​

Write the equation in general form. ​

The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 42 mph. Round your answer to the nearest integer. ​

The table that follows gives the population of a city. Find the power function that best fits the data, with x equal to the number of years past 1950. According to the model, will the city's population be greater than 1,400 by the year 2010? Round your final answer to three decimal places.

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. ​

Factor the function . ​

The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. ​

Assume that costs and expenses for Continental Divide Mining can be described by and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs. ​

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

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

Sketch the graph of the function . ​

Solve the equation below using quadratic methods. ​ ​

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? ​

The given graph shows the cost C, in thousands of dollars, of a production run for a product when x machines are used. Estimate the company's fixed cost of production to the nearest thousand dollars, and determine the number of machines that will result in maximum cost for the company. ​ ​

Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by and . ​

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

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,600?

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. Round your answers to two decimal places.

Sketch the graph of the following function by using graphing calculator.

Sketch the graph of the function .

Solve the equation by using the quadratic formula. Give real solutions only.

Write the equation in general form.

The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 42 mph. Round your answer to the nearest integer.

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.

Factor the function .

The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity.

Assume that costs and expenses for Continental Divide Mining can be described by and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs.

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

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

Sketch the graph of the function .

Solve the equation below using quadratic methods.

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?

The given graph shows the cost C, in thousands of dollars, of a production run for a product when x machines are used. Estimate the company's fixed cost of production to the nearest thousand dollars, and determine the number of machines that will result in maximum cost for the company.

Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by and .