Question 1

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 2

For the function given below, determine the domain, all x-intercepts, and find any vertical and slant asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function on the axes provided.

Accepted Answer

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

Question 3

If   is a root of   , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

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

Question 4

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 5

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 6

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 7

Use long division to divide.

Accepted Answer

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

Question 8

Find all the real zeros of   .

Accepted Answer

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

Question 9

Match the equation with its graph.

Accepted Answer

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

Question 10

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 11

Use synthetic division to divide.

Accepted Answer

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

Question 12

Given   is a root, determine all other roots of   .

Accepted Answer

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

Question 13

Use the zero or root feature of a graphing utility to approximate the zeros of   accurate to the nearest thousandth.

Accepted Answer

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

Question 14

Consider the function   . Identify any slant asymptotes.

Accepted Answer

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

Question 15

Find the zeros (if any) of the rational function   .

Accepted Answer

A)    and   
B)    
C)    
D)    
E) There are no zeros. 
A)    and   
B)    
C)    
D)    
E) There are no zeros.

Question 16

Using the factors   and   , find the remaining factor(s) of   and write the polynomial in fully factored form.

Accepted Answer

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

Question 17

Find all real solutions of the polynomial equation   .

Accepted Answer

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

Question 18

Identify the function whose graph is provided.

Accepted Answer

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

Question 19

Suppose the cost C (in millions of dollars) of cleaning p% of an oil spill from a particular lake is estimated by   ,   Find the cost of cleaning up   of the spill. Round to the nearest tenth of a million dollars.

Accepted Answer

A) 10 
B) 55.7 
C) 90 
D) 170 
E) 5.3 
A) 10 
B) 55.7 
C) 90 
D) 170 
E) 5.3

Question 20

Find real numbers a and b such that the equation   is true.

Accepted Answer

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

Simplify and write the answer in standard form.

For the function given below, determine the domain, all x-intercepts, and find any vertical and slant asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function on the axes provided.

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify and write the answer in standard form.

Simplify and write the answer in standard form.

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

Use long division to divide.

Find all the real zeros of .

Match the equation with its graph.

Simplify and write the answer in standard form.

Use synthetic division to divide.

Given is a root, determine all other roots of .

Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.

Consider the function . Identify any slant asymptotes.

Find the zeros (if any) of the rational function .

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Find all real solutions of the polynomial equation .

Identify the function whose graph is provided.

Suppose the cost C (in millions of dollars) of cleaning p% of an oil spill from a particular lake is estimated by , Find the cost of cleaning up of the spill. Round to the nearest tenth of a million dollars.

Find real numbers a and b such that the equation is true.

Prerequisites

Functions and Their Graphs

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 3: Polynomial and Rational Functions

Simplify and write the answer in standard form.

For the function given below, determine the domain, all x-intercepts, and find any vertical and slant asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function on the axes provided.

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify and write the answer in standard form.

Simplify and write the answer in standard form.

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

Use long division to divide.

Find all the real zeros of .

Match the equation with its graph.

Simplify and write the answer in standard form.

Use synthetic division to divide.

Given is a root, determine all other roots of .

Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.

Consider the function . Identify any slant asymptotes.

Find the zeros (if any) of the rational function .

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Find all real solutions of the polynomial equation .

Identify the function whose graph is provided.

Suppose the cost C (in millions of dollars) of cleaning p% of an oil spill from a particular lake is estimated by , Find the cost of cleaning up of the spill. Round to the nearest tenth of a million dollars.

Find real numbers a and b such that the equation is true.

Prerequisites

Functions and Their Graphs

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters