Question 1

Determine the vertex of the graph of the quadratic function   .

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Use synthetic division to divide.

Accepted Answer

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B)    
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E)    
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B)    
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D)    
E)

Question 4

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

Accepted Answer

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D)    
E)

Question 5

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 6

Write the complex number   in standard form.

Accepted Answer

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B)    
C)    
D)    
E)    
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E)

Question 7

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

Accepted Answer

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

Question 8

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

Question 9

Use long division to divide.

Accepted Answer

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

Question 10

Find all zeros of the function   .

Accepted Answer

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Question 11

Combine   and write the answer in standard form.

Accepted Answer

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E)

Question 12

Simplify   and write the answer in standard form.

Accepted Answer

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D)    
E) The expression cannot be simplified. 
A)    
B)    
C)    
D)    
E) The expression cannot be simplified.

Question 13

Write   as a product of linear factors.

Accepted Answer

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

Question 14

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 15

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Write the quadratic function,   , in standard form.

Accepted Answer

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

Question 19

Use synthetic division to divide.

Accepted Answer

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

Question 20

Find all real solutions of the polynomial equation   .

Accepted Answer

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

Determine the vertex of the graph of the quadratic function .

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

Use synthetic division to divide.

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

Compare the graph of with .

Write the complex number in standard form.

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

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

Use long division to divide.

Find all zeros of the function .

Combine and write the answer in standard form.

Simplify and write the answer in standard form.

Write as a product of linear factors.

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

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

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

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

Write the quadratic function, , in standard form.

Use synthetic division to divide.

Find all real solutions of the polynomial equation .

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

Determine the vertex of the graph of the quadratic function .

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

Use synthetic division to divide.

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

Compare the graph of with .

Write the complex number in standard form.

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

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

Use long division to divide.

Find all zeros of the function .

Combine and write the answer in standard form.

Simplify and write the answer in standard form.

Write as a product of linear factors.

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

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

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

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

Write the quadratic function, , in standard form.

Use synthetic division to divide.

Find all real solutions of the polynomial equation .

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