Question 1

Find the x-intercepts, if any exist. Round your answers to two decimal places. ​   ​

Accepted Answer

A)  x-intercepts:   ,   
B)  x-intercepts:   ,   
C)  x-intercepts:   ,   
D)  x-intercepts:   ,   
E)  no x-intercepts 
A)  x-intercepts:   ,   
B)  x-intercepts:   ,   
C)  x-intercepts:   ,   
D)  x-intercepts:   ,   
E)  no x-intercepts

Question 2

The table below shows the national expenditures for health care in a certain country for selected years. Find a power model and a linear model for the data where x is the number of years after 1950. Which of the models seems to be the best to use if you are interested in finding the health care costs near the year 1990? Round numerical values in your answers to three decimal places. ​

Accepted Answer

A)      The power model gives more accurate results near the year 1990. 
B)      The linear model gives more accurate results near the year 1990. 
C)      The power model gives more accurate results near the year 1990. 
D)      The linear model gives more accurate results near the year 1990. 
E)      The power model gives more accurate results near the year 1990. 
A)      The power model gives more accurate results near the year 1990. 
B)      The linear model gives more accurate results near the year 1990. 
C)      The power model gives more accurate results near the year 1990. 
D)      The linear model gives more accurate results near the year 1990. 
E)      The power model gives more accurate results near the year 1990.

Question 3

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 4

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 5

Sketch the graph of the function below. ​   ​

Accepted Answer

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

Question 6

Sketch the graph of the function   . ​

Accepted Answer

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

Question 7

If   , find   and   . 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 8

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)  $1,701 
B)  $2,613 
C)  $808 
D)  $95 
E)  $185 
A)  $1,701 
B)  $2,613 
C)  $808 
D)  $95 
E)  $185

Question 9

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 10

Find the maximum revenue for the revenue function   . Round your answer to the nearest cent. ​

Accepted Answer

A)  $84,008.93 
B)  $252,026.79 
C)  $48,005.10 
D)  $216,022.96 
E)  $253,026.79 
A)  $84,008.93 
B)  $252,026.79 
C)  $48,005.10 
D)  $216,022.96 
E)  $253,026.79

Question 11

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 12

If the profit from the sale of x units of a product is   , what level(s) of production will yield a profit of $1,000? ​

Accepted Answer

A)  less 15 units of production. 
B)  more than 80 units of production. 
C)  95 units of production. 
D)  65 units of production. 
E)  15 or 80 units of production. 
A)  less 15 units of production. 
B)  more than 80 units of production. 
C)  95 units of production. 
D)  65 units of production. 
E)  15 or 80 units of production.

Question 13

If the supply function for a commodity is   and the demand function is   , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places. ​

Accepted Answer

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

Question 14

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 15

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 16

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 17

The table shows the average earnings of year-round, full-time workers by gender and educational attainment in a certain country. Let x represent earnings for males and y represent earnings for females, and find a linear model that expresses women's annual earnings as a function of men's. Interpret the slope of the linear model. Round your final values to three decimal places. ​

Accepted Answer

A)    slope: females earn $1,296 for each $1,000 males earn 
B)    slope: the average difference in yearly male and female earnings is $1,296 
C)    slope: females earn $652 for each $1,000 males earn 
D)    slope: the average difference in yearly male and female earnings is $652 
E)    slope: the average of male and female earnings increases by an average of $652 for each level of educational attainment 
A)    slope: females earn $1,296 for each $1,000 males earn 
B)    slope: the average difference in yearly male and female earnings is $1,296 
C)    slope: females earn $652 for each $1,000 males earn 
D)    slope: the average difference in yearly male and female earnings is $652 
E)    slope: the average of male and female earnings increases by an average of $652 for each level of educational attainment

Question 18

Sketch the graph of the function   . ​

Accepted Answer

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

Question 19

Write the equation   in general form. ​

Accepted Answer

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

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)

Find the x-intercepts, if any exist. Round your answers to two decimal places.

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

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.

Sketch the graph of the function below.

Sketch the graph of the function .

If , find and . Round your answers to two decimal places.

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.

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.

Find the maximum revenue for the revenue function . Round your answer to the nearest cent.

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.

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,000?

If the supply function for a commodity is and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places.

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

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.

Sketch the graph of the function .

Write the equation in general form.

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

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

Find the x-intercepts, if any exist. Round your answers to two decimal places. ​ ​

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

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. ​

Sketch the graph of the function below. ​ ​

Sketch the graph of the function . ​

If , find and . Round your answers to two decimal places. ​

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. ​

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. ​ ​

Find the maximum revenue for the revenue function . Round your answer to the nearest cent. ​

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. ​ ​

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,000? ​

If the supply function for a commodity is and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places. ​

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

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. ​

Sketch the graph of the function . ​

Write the equation in general form. ​

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

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

Find the x-intercepts, if any exist. Round your answers to two decimal places.

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

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.

Sketch the graph of the function below.

Sketch the graph of the function .

If , find and . Round your answers to two decimal places.

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.

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.

Find the maximum revenue for the revenue function . Round your answer to the nearest cent.

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.

If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,000?

If the supply function for a commodity is and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places.

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

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.

Sketch the graph of the function .

Write the equation in general form.

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