Question 1

Determine the value of k so that the divisor is a factor of the dividend.

Accepted Answer

A) 24 
B) 48 
C) 18 
D) -24 
E) -48 
A) 24 
B) 48 
C) 18 
D) -24 
E) -48

Question 2

The cost, in dollars, of producing x golf balls is given by   . The average cost per golf ball is given by   . Find the average cost of producing   golf balls.

Accepted Answer

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

Question 3

Given   is a zero of the polynomial function   , find the remaining zeros of the polynomial.

Accepted Answer

A)    
B)    
C)    
D)    
E) 5 i, -5, 4 + i , 4 - i 
A)    
B)    
C)    
D)    
E) 5 i, -5, 4 + i , 4 - i

Question 4

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of the polynomial function below.

Accepted Answer

A) upper bound 2, lower bound -5 
B) upper bound 3, lower bound -5 
C) upper bound 2, lower bound -1 
D) upper bound 1, lower bound -1 
E) upper bound 3, lower bound -1 
A) upper bound 2, lower bound -5 
B) upper bound 3, lower bound -5 
C) upper bound 2, lower bound -1 
D) upper bound 1, lower bound -1 
E) upper bound 3, lower bound -1

Question 5

A rectangular box has a volume of   cubic inches. The height of the box is   inches. The width of the box is   inches. Find the length of the box in terms of x .

Accepted Answer

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

Question 6

Find all of the zeros of the polynomial function   and state the multiplicity of each zero.

Accepted Answer

A) 16, multiplicity of 2 6, multiplicity of 1 
B) -4, multiplicity of 2 4, multiplicity of 2 -6, multiplicity of 1 
C) -4, multiplicity of 1 4, multiplicity of 1 6, multiplicity of 3 
D) -16, multiplicity of 1 -6, multiplicity of 3 
E) 4, multiplicity of 2 -6, multiplicity of 1 
A) 16, multiplicity of 2 6, multiplicity of 1 
B) -4, multiplicity of 2 4, multiplicity of 2 -6, multiplicity of 1 
C) -4, multiplicity of 1 4, multiplicity of 1 6, multiplicity of 3 
D) -16, multiplicity of 1 -6, multiplicity of 3 
E) 4, multiplicity of 2 -6, multiplicity of 1

Question 7

Find all vertical asymptotes of the rational function below.

Accepted Answer

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

Question 8

Determine the vertical and horizontal asymptotes of the rational function below.

Accepted Answer

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

Question 9

Find a polynomial function P with real coefficients that is degree 3, has zeros   and   and   .

Accepted Answer

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

Question 10

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation   .

Accepted Answer

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

Question 11

The number of ways one can select three cards from a group of n cards (assuming the order of the selection matters), where   , is given by   . For a certain card trick a magician has determined that there are exactly 5814 ways to choose three cards from a given group. How many cards are in the group?

Accepted Answer

A) 18 cards 
B) 17 cards 
C) 19 cards 
D) 20 cards 
E) 21 cards 
A) 18 cards 
B) 17 cards 
C) 19 cards 
D) 20 cards 
E) 21 cards

Question 12

Find the horizontal asymptote of the rational function   .

Accepted Answer

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

Question 13

Use synthetic division and the Factor Theorem to determine whether or not   is a factor of   .

Accepted Answer

A) Yes,   is a factor. 
B) No,   is not a factor. 
A) Yes,   is a factor. 
B) No,   is not a factor.

Question 14

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 15

The cost, in dollars, of producing x golf balls is given by   . The average cost per golf ball is given by   . Find the average cost per ball as the number of golf balls produced increases.

Accepted Answer

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

Question 16

Determine the vertical and horizontal asymptotes of the rational function below.

Accepted Answer

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

Question 17

A company constructs boxes from rectangular pieces of cardboard that measure 10 inches by 11 inches. An open box is formed by cutting squares that measure x inches by x inches from each corner of the cardboard and folding up the sides. Express the volume V of the box as a function of x .

Accepted Answer

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

Question 18

Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function   .

Accepted Answer

A) down to the far left, up to the far right 
B) down to the far left, down to the far right 
C) up to the far left, up to the far right 
D) up to the far left, down to the far right 
E) cannot be determined 
A) down to the far left, up to the far right 
B) down to the far left, down to the far right 
C) up to the far left, up to the far right 
D) up to the far left, down to the far right 
E) cannot be determined

Question 19

The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 1496 cubic inches, find the dimensions of the box.

Accepted Answer

A) 373 in. by 747 in. by 376 in. 
B) 7 in. by 15 in. by 10 in. 
C) 8.5 in. by 18 in. by 11.5 in. 
D) 8 in. by 17 in. by 11 in. 
E) 370 in. by 741 in. by 373 in. 
A) 373 in. by 747 in. by 376 in. 
B) 7 in. by 15 in. by 10 in. 
C) 8.5 in. by 18 in. by 11.5 in. 
D) 8 in. by 17 in. by 11 in. 
E) 370 in. by 741 in. by 373 in.

Question 20

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by   where t is the number of months after the CD is released. Find the monthly sales the company expects   months after the CD is released. Round to the nearest 100 CDs.

Accepted Answer

A) 3700 CDs 
B) 3500 CDs 
C) 3400 CDs 
D) 4300 CDs 
E) 2900 CDs 
A) 3700 CDs 
B) 3500 CDs 
C) 3400 CDs 
D) 4300 CDs 
E) 2900 CDs

Determine the value of k so that the divisor is a factor of the dividend.

The cost, in dollars, of producing x golf balls is given by . The average cost per golf ball is given by . Find the average cost of producing golf balls.

Given is a zero of the polynomial function , find the remaining zeros of the polynomial.

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of the polynomial function below.

A rectangular box has a volume of cubic inches. The height of the box is inches. The width of the box is inches. Find the length of the box in terms of x .

Find all of the zeros of the polynomial function and state the multiplicity of each zero.

Find all vertical asymptotes of the rational function below.

Determine the vertical and horizontal asymptotes of the rational function below.

Find a polynomial function P with real coefficients that is degree 3, has zeros and and .

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation .

The number of ways one can select three cards from a group of n cards (assuming the order of the selection matters), where , is given by . For a certain card trick a magician has determined that there are exactly 5814 ways to choose three cards from a given group. How many cards are in the group?

Find the horizontal asymptote of the rational function .

Use synthetic division and the Factor Theorem to determine whether or not is a factor of .

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

The cost, in dollars, of producing x golf balls is given by . The average cost per golf ball is given by . Find the average cost per ball as the number of golf balls produced increases.

Determine the vertical and horizontal asymptotes of the rational function below.

A company constructs boxes from rectangular pieces of cardboard that measure 10 inches by 11 inches. An open box is formed by cutting squares that measure x inches by x inches from each corner of the cardboard and folding up the sides. Express the volume V of the box as a function of x .

Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function .

The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 1496 cubic inches, find the dimensions of the box.

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by where t is the number of months after the CD is released. Find the monthly sales the company expects months after the CD is released. Round to the nearest 100 CDs.

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

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Exam 3: Polynomial and Rational Functions

Determine the value of k so that the divisor is a factor of the dividend.

The cost, in dollars, of producing x golf balls is given by . The average cost per golf ball is given by . Find the average cost of producing golf balls.

Given is a zero of the polynomial function , find the remaining zeros of the polynomial.

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of the polynomial function below.

A rectangular box has a volume of cubic inches. The height of the box is inches. The width of the box is inches. Find the length of the box in terms of x .

Find all of the zeros of the polynomial function and state the multiplicity of each zero.

Find all vertical asymptotes of the rational function below.

Determine the vertical and horizontal asymptotes of the rational function below.

Find a polynomial function P with real coefficients that is degree 3, has zeros and and .

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation .

The number of ways one can select three cards from a group of n cards (assuming the order of the selection matters), where , is given by . For a certain card trick a magician has determined that there are exactly 5814 ways to choose three cards from a given group. How many cards are in the group?

Find the horizontal asymptote of the rational function .

Use synthetic division and the Factor Theorem to determine whether or not is a factor of .

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

The cost, in dollars, of producing x golf balls is given by . The average cost per golf ball is given by . Find the average cost per ball as the number of golf balls produced increases.

Determine the vertical and horizontal asymptotes of the rational function below.

A company constructs boxes from rectangular pieces of cardboard that measure 10 inches by 11 inches. An open box is formed by cutting squares that measure x inches by x inches from each corner of the cardboard and folding up the sides. Express the volume V of the box as a function of x .

Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function .

The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 1496 cubic inches, find the dimensions of the box.

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by where t is the number of months after the CD is released. Find the monthly sales the company expects months after the CD is released. Round to the nearest 100 CDs.

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters