Question 1

​Analytically determine the location of any vertical asymptotes. ​  ​
​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​no vertical asymptotes

Question 2

Graph a function on the interval  having the following characteristics. Absolute maximum at  Absolute minimum at  Relative minimum at  Relative maximum at  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 3

Copy the points (-2,5),(3,-5),(-4,-1),(4,0),(2,-3)in the Cartesian plane. ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 4

​A firm can produce 100 units per week.If its total cost function is  dollars,and its total revenue function is  dollars,how many units x should it produce to maximize its profit? ​

Accepted Answer

A)  ​1250 units 
B)  ​650 units 
C)  ​97 units 
D)  ​50 units 
E)  ​100 units

Question 5

​Assume that the median sales prices of existing one family homes sold (in thousands of dollars)in the United States from 1990 through 2005 are as given in the following figure.Use the following figure to estimate the percent increase in the value of existing one-family homes from1999 to 2000.Round your answer to the nearest hundredth if necessary. ​
​  ​

Accepted Answer

A)  ​1.2% 
B)  ​201.21% 
C)  ​101.21% 
D)  ​98.8% 
E)  ​1.21%

Question 6

​The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by  Find the rate of change in the number of decibels when the intensity is  watt per square centimeter.Round your answer to the nearest decibel.

Accepted Answer

A)  ​317 decibels per watt per square cm 
B)  ​25,645 decibels per watt per square cm 
C)  ​2,849 decibels per watt per square cm 
D)  ​230,802 decibels per watt per square cm 
E)  ​2,851 decibels per watt per square cm

Question 7

​Find the derivative of the function  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 8

​Use a graphing utility to graph the function

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 9

​The cost C (in millions of dollars)for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by  ,for  Find the limit of C as  ​

Accepted Answer

A)  ​540 
B)  ​100 
C)  ​-100 
D)  ​∞ 
E)  ​0

Question 10

Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line. ​
Point: ​  Line:  ​

Accepted Answer

A)  ​(i) parallel: 
(ii) perpendicular:  
B)  ​(i) parallel: 
(ii) perpendicular:  
C)  ​​(i) parallel: 
(ii) perpendicular:  
D)  ​​(i) parallel: 
(ii) perpendicular:  
E)  ​​(i)parallel: 
(ii)perpendicular:

Question 11

​Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by  Find the rate of change of y with respect to x when  and  ​

Accepted Answer

A)  ​-2 
B)  ​0 
C)  ​3 
D)  ​-7 
E)  ​5

Question 12

​How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places. ​

Accepted Answer

A)  ​2.95 years 
B)  ​2.70 years 
C)  ​0.56 years 
D)  3.38​ years 
E)  ​2.56 years

Question 13

Determine whether y is a function of x. ​
​  ​

Accepted Answer

A)  ​Yes 
B)  ​No

Question 14

​Find the rate of change of x with respect to p. ​  ,  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 15

​Find  ,if  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 16

​Find the y-value at the relative minima,and use a graphing utility to check your result. ​  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​does not exist

Question 17

​Find the points of inflection and discuss the concavity of the function. ​​
​  ​

Accepted Answer

A)  ​inflection point at  ; concave downward on  ; concave upward on  
B)  ​inflection point at  ; concave upward on  ; concave downward on  
C)  ​​inflection point at  ; concave downward on  ; concave upward on  
D)  ​inflection point at  ; concave upward on  ; concave downward on  
E)  ​none of the above

Question 18

Evaluate (if possible)the function at the given value of the independent variable.Simplify the results. ​  ,  ​

Accepted Answer

A)  101 
B)  109 
C)  -11 
D)  -3 
E)  undefined

Question 19

​A small business recaps and sells tires.The business has a revenue function  and a cost function  ,where x represents the number of sets of four tires recapped and sold.Find the number of sets of recaps that must be sold to break even. ​

Accepted Answer

A)  ​100 
B)  ​300 
C)  ​6 
D)  ​200 
E)  ​65

Question 20

Find the derivative of the function. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 1: Functions, graphs, and Limits

Analytically determine the location of any vertical asymptotes.

Graph a function on the interval having the following characteristics. Absolute maximum at Absolute minimum at Relative minimum at Relative maximum at

Copy the points (-2,5) ,(3,-5) ,(-4,-1) ,(4,0) ,(2,-3) in the Cartesian plane.

A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,how many units x should it produce to maximize its profit?

The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

Find the derivative of the function

Use a graphing utility to graph the function

The cost C (in millions of dollars) for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by ,for Find the limit of C as

Write an equation of the line that passes through the point (i) parallel to the given line,and (ii) perpendicular to the given line. Point: Line:

Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and

How long (in years) would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places.

Determine whether y is a function of x.

Find the rate of change of x with respect to p. ,

Find ,if

Find the y-value at the relative minima,and use a graphing utility to check your result.

Find the points of inflection and discuss the concavity of the function.

Evaluate (if possible) the function at the given value of the independent variable.Simplify the results. ,

A small business recaps and sells tires.The business has a revenue function and a cost function ,where x represents the number of sets of four tires recapped and sold.Find the number of sets of recaps that must be sold to break even.

Find the derivative of the function.

Exam 1: Functions, graphs, and Limits

​Analytically determine the location of any vertical asymptotes. ​ ​ ​

Graph a function on the interval having the following characteristics. Absolute maximum at Absolute minimum at Relative minimum at Relative maximum at ​

Copy the points (-2,5) ,(3,-5) ,(-4,-1) ,(4,0) ,(2,-3) in the Cartesian plane. ​

​A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,how many units x should it produce to maximize its profit? ​

​The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

​Find the derivative of the function ​

​Use a graphing utility to graph the function

​The cost C (in millions of dollars) for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by ,for Find the limit of C as ​

Write an equation of the line that passes through the point (i) parallel to the given line,and (ii) perpendicular to the given line. ​ Point: ​ Line: ​

​Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and ​

​How long (in years) would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places. ​

Determine whether y is a function of x. ​ ​ ​

​Find the rate of change of x with respect to p. ​ , ​

​Find ,if ​

​Find the y-value at the relative minima,and use a graphing utility to check your result. ​ ​

​Find the points of inflection and discuss the concavity of the function. ​​ ​ ​

Evaluate (if possible) the function at the given value of the independent variable.Simplify the results. ​ , ​

​A small business recaps and sells tires.The business has a revenue function and a cost function ,where x represents the number of sets of four tires recapped and sold.Find the number of sets of recaps that must be sold to break even. ​

Find the derivative of the function. ​ ​

Analytically determine the location of any vertical asymptotes.

Graph a function on the interval having the following characteristics. Absolute maximum at Absolute minimum at Relative minimum at Relative maximum at

Copy the points (-2,5) ,(3,-5) ,(-4,-1) ,(4,0) ,(2,-3) in the Cartesian plane.

A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,how many units x should it produce to maximize its profit?

The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

Find the derivative of the function

Use a graphing utility to graph the function

The cost C (in millions of dollars) for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by ,for Find the limit of C as

Write an equation of the line that passes through the point (i) parallel to the given line,and (ii) perpendicular to the given line. Point: Line:

Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and

How long (in years) would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places.

Determine whether y is a function of x.

Find the rate of change of x with respect to p. ,

Find ,if

Find the y-value at the relative minima,and use a graphing utility to check your result.

Find the points of inflection and discuss the concavity of the function.

Evaluate (if possible) the function at the given value of the independent variable.Simplify the results. ,

A small business recaps and sells tires.The business has a revenue function and a cost function ,where x represents the number of sets of four tires recapped and sold.Find the number of sets of recaps that must be sold to break even.

Find the derivative of the function.