Question 1

Find the standard form of the quadratic function shown below:

Accepted Answer

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

Question 2

Simplify:

Accepted Answer

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

Question 3

From the graph of the quadratic function   , determine the equation of the axis of symmetry.

Accepted Answer

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

Question 4

Use the quadratic formula to solve   .

Accepted Answer

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

Question 5

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 6

Determine the x-intercept(s) of the quadratic function   .

Accepted Answer

A)    
B)    
C)    
D)    
E) no x-intercept(s) 
A)    
B)    
C)    
D)    
E) no x-intercept(s)

Question 7

Use long division to divide.

Accepted Answer

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

Question 8

Given   is a root, determine all other roots of   .

Accepted Answer

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

Question 9

Determine the x-intercept(s) of the quadratic function   .

Accepted Answer

A)    
B)    
C)    
D)    
E) no x-intercept(s) 
A)    
B)    
C)    
D)    
E) no x-intercept(s)

Question 10

Write   in the form   when   .

Accepted Answer

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

Question 11

Consider the function   . Find the function's domain and identify any horizontal and vertical asymptotes.

Accepted Answer

A) domain: all real numbers x except for   and   ; vertical asymptote:   ; horizontal asymptote:   
B) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
C) domain: all real numbers x except for   ; vertical asymptotes:   and   ; horizontal asymptote: none 
D) domain: all real numbers x except for   and   ; vertical asymptotes:   and   ; horizontal asymptote:   
E) domain: all real numbers x except for   and   ; vertical asymptote:   ; horizontal asymptote: none 
A) domain: all real numbers x except for   and   ; vertical asymptote:   ; horizontal asymptote:   
B) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
C) domain: all real numbers x except for   ; vertical asymptotes:   and   ; horizontal asymptote: none 
D) domain: all real numbers x except for   and   ; vertical asymptotes:   and   ; horizontal asymptote:   
E) domain: all real numbers x except for   and   ; vertical asymptote:   ; horizontal asymptote: none

Question 12

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

Accepted Answer

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

Question 13

Find two positive real numbers whose product is a maximum and whose sum is   .

Accepted Answer

A)    
B)    
C)    
D)    
E) 58, 82 
A)    
B)    
C)    
D)    
E) 58, 82

Question 14

Write the standard form of the equation of the parabola that has a vertex at   and passes through the point   .

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Write   as a product of linear factors.

Accepted Answer

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

Question 17

Find all the rational zeros of the function   .

Accepted Answer

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

Question 18

Use synthetic division to divide.

Accepted Answer

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

Question 19

Consider the function   . Find the function's domain and identify any horizontal and vertical asymptotes.

Accepted Answer

A) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
B) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
C) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
D) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
E) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
A) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
B) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
C) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
D) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:   
E) domain: all real numbers x except for   ; vertical asymptote:   ; horizontal asymptote:

Question 20

Combine   and write the answer in standard form.

Accepted Answer

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

Find the standard form of the quadratic function shown below:

Simplify:

From the graph of the quadratic function , determine the equation of the axis of symmetry.

Use the quadratic formula to solve .

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

Determine the x-intercept(s) of the quadratic function .

Use long division to divide.

Given is a root, determine all other roots of .

Determine the x-intercept(s) of the quadratic function .

Write in the form when .

Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.

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

Find two positive real numbers whose product is a maximum and whose sum is .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

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

Write as a product of linear factors.

Find all the rational zeros of the function .

Use synthetic division to divide.

Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.

Combine and write the answer in standard form.

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

Find the standard form of the quadratic function shown below:

Simplify:

From the graph of the quadratic function , determine the equation of the axis of symmetry.

Use the quadratic formula to solve .

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

Determine the x-intercept(s) of the quadratic function .

Use long division to divide.

Given is a root, determine all other roots of .

Determine the x-intercept(s) of the quadratic function .

Write in the form when .

Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.

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

Find two positive real numbers whose product is a maximum and whose sum is .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

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

Write as a product of linear factors.

Find all the rational zeros of the function .

Use synthetic division to divide.

Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.

Combine and write the answer in standard form.

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