Question 1

The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.

Accepted Answer

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

Question 2

Determine the domain of

Accepted Answer

A)  all real numbers except   
B)  all real numbers except   
C)  all real numbers except   
D)  all real numbers except   
E)  all real numbers 
A)  all real numbers except   
B)  all real numbers except   
C)  all real numbers except   
D)  all real numbers except   
E)  all real numbers

Question 3

Find an equation of the parabola that has a vertex at   and whose graph passes through the point

Accepted Answer

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

Question 4

The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by   Find the maximum height of the projectile.

Accepted Answer

A)  254 ft 
B)  219 ft 
C)  263 ft 
D)  105 ft 
E)  315 ft 
A)  254 ft 
B)  219 ft 
C)  263 ft 
D)  105 ft 
E)  315 ft

Question 5

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 6

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below.   Find a quadratic model for these data.

Accepted Answer

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

Question 7

Sketch the graph of the polynomial function   Do not use a graphing calculator.

Accepted Answer

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

Question 8

A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Accepted Answer

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

Question 9

Find the real zeros of the polynomial function   and determine the multiplicity of each.

Accepted Answer

A)    , multiplicity 2;   , multiplicity 3 
B)    , multiplicity 2;   , multiplicity 1;   , multiplicity 2 
C)    , multiplicity 3;   , multiplicity 2 
D)    , multiplicity 3;   , multiplicity 2 
E)    , multiplicity 2;   , multiplicity 2;   , multiplicity 1 
A)    , multiplicity 2;   , multiplicity 3 
B)    , multiplicity 2;   , multiplicity 1;   , multiplicity 2 
C)    , multiplicity 3;   , multiplicity 2 
D)    , multiplicity 3;   , multiplicity 2 
E)    , multiplicity 2;   , multiplicity 2;   , multiplicity 1

Question 10

Use the zero   of   to find all the zeros of f.

Accepted Answer

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

Question 11

Describe the right-hand and the left-hand behavior of the graph of

Accepted Answer

A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
D)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. 
A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
D)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question 12

The path of a diver is given by   where   is the height (in feet) and   is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.

Accepted Answer

A)  12 feet 
B)  13 feet 
C)  10 feet 
D)  14 feet 
E)  17 feet 
A)  12 feet 
B)  13 feet 
C)  10 feet 
D)  14 feet 
E)  17 feet

Question 13

Find all real zeros of the polynomial   and determine the mutiplicity of each.

Accepted Answer

A)    , multiplicity 2;   , multiplicity 2 
B)    , multiplicity 2;   , multiplicity 2 
C)    , multiplicity 2;   , multiplicity 1 
D)    , multiplicity 2;   , multiplicity 2 
E)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1;   , multiplicity 1 
A)    , multiplicity 2;   , multiplicity 2 
B)    , multiplicity 2;   , multiplicity 2 
C)    , multiplicity 2;   , multiplicity 1 
D)    , multiplicity 2;   , multiplicity 2 
E)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1;   , multiplicity 1

Question 14

The demand for a stethoscope is given by where p is the unit price ( in dollar) and x is the number of units.The total revenue R (in dollars) obtained by producing ans selling x units given by the model     Write and solve an equation to determine a price that yields revenue of $50 million.Use a graphing utility to verify your result.

Accepted Answer

A)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $50 million. 
B)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $75 million. 
C)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $25 million. 
D)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $60 million. 
E)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $80 million. 
A)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $50 million. 
B)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $75 million. 
C)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $25 million. 
D)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $60 million. 
E)  Because the solutions are imaginary, there is no quantity of units x or price p that will yield a revenue of $80 million.

Question 15

Find all the real zeros of the polynomial function   and determine the multiplicity of each.

Accepted Answer

A)    , multiplicity 2;   , multiplicity 1 
B)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1 
C)    , multiplicity 2;   , multiplicity 1 
D)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1 
E)    , multiplicity 3 
A)    , multiplicity 2;   , multiplicity 1 
B)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1 
C)    , multiplicity 2;   , multiplicity 1 
D)    , multiplicity 1;   , multiplicity 1;   , multiplicity 1 
E)    , multiplicity 3

Question 16

A company that produces video games estimates that the profit   (in dollars) for selling a new game is given by     where   is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.

Accepted Answer

A)  $399,893 or $744,397 
B)  $433,844 or $721,190 
C)  $315,902 or $794,255 
D)  $368,914 or $764,017 
E)  $344,417 or $778,509 
A)  $399,893 or $744,397 
B)  $433,844 or $721,190 
C)  $315,902 or $794,255 
D)  $368,914 or $764,017 
E)  $344,417 or $778,509

Question 17

Sketch the graph of the rational function.Check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes.

Accepted Answer

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

Question 18

Compare the graph of   with

Accepted Answer

A)    shifts right   units, shifts downward   units, and shrinks by a factor of   
B)    shifts right   units, shifts upward   units, and stretches by a factor of   
C)    shifts left   units, shifts downward   units, and stretches by a factor of   
D)    shifts right   units, shifts upward   units, and shrinks by a factor of   
E)    shifts left   units, shifts upward   units, and stretches by a factor of   
A)    shifts right   units, shifts downward   units, and shrinks by a factor of   
B)    shifts right   units, shifts upward   units, and stretches by a factor of   
C)    shifts left   units, shifts downward   units, and stretches by a factor of   
D)    shifts right   units, shifts upward   units, and shrinks by a factor of   
E)    shifts left   units, shifts upward   units, and stretches by a factor of

Question 19

Use synthetic division to divide.

Accepted Answer

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

Question 20

Write   as a product of linear factors given that   and   are zeros of the polynomial.

Accepted Answer

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

The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.

Determine the domain of

Find an equation of the parabola that has a vertex at and whose graph passes through the point

The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by Find the maximum height of the projectile.

Simplify and write the answer in standard form.

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data.

Sketch the graph of the polynomial function Do not use a graphing calculator.

A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Find the real zeros of the polynomial function and determine the multiplicity of each.

Use the zero of to find all the zeros of f.

Describe the right-hand and the left-hand behavior of the graph of

The path of a diver is given by where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.

Find all real zeros of the polynomial and determine the mutiplicity of each.

Find all the real zeros of the polynomial function and determine the multiplicity of each.

Sketch the graph of the rational function.Check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes.

Compare the graph of with

Use synthetic division to divide.

Write as a product of linear factors given that and are zeros of the polynomial.

Fundamental Concepts of Algebra

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Functions and Graphs

Exponential and Logarithmic Functions

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Exam 3: Polynomial and Rational Functions

The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.

Determine the domain of

Find an equation of the parabola that has a vertex at and whose graph passes through the point

The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by Find the maximum height of the projectile.

Simplify and write the answer in standard form.

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data.

Sketch the graph of the polynomial function Do not use a graphing calculator.

A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Find the real zeros of the polynomial function and determine the multiplicity of each.

Use the zero of to find all the zeros of f.

Describe the right-hand and the left-hand behavior of the graph of

The path of a diver is given by where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.

Find all real zeros of the polynomial and determine the mutiplicity of each.

Find all the real zeros of the polynomial function and determine the multiplicity of each.

Sketch the graph of the rational function.Check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes.

Compare the graph of with

Use synthetic division to divide.

Write as a product of linear factors given that and are zeros of the polynomial.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

Filters