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Deck 3: Polynomial and Rational Functions
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Question
From the graph of the quadratic function 
, determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
Question
Write the quadratic function, 
, in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
Question
From the graph of the quadratic function 
, determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
Question
Find the standard form of the quadratic function shown below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find two positive real numbers whose product is a maximum and whose sum is 
.
A)
B)
C)
D)
E)58, 82
.A)
B)
C)
D)
E)58, 82
Question
Write the standard form of the equation of the parabola that has a vertex at 
and passes through the point 
.
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
Question
Write the quadratic function, 
, in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
Question
Determine the x-intercept(s) of the quadratic function 
.
A)
B)
C)
D)
E)no x-intercept(s)
.A)
B)
C)
D)
E)no x-intercept(s)
Question
Describe the right-hand and the left-hand behavior of the graph of 
.
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
Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Compare the graph of 
with 
.
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 
.
with .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
Describe the right-hand and the left-hand behavior of the graph of 
.
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
Using a graphing utility, graph 
and approximate the zeros and their multiplicity.
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
and approximate the zeros and their multiplicity.A)
, multiplicity 2; , multiplicity 3B)
, multiplicity 2; , multiplicity 1; , multiplicity 2C)
, multiplicity 3; , multiplicity 2D)
, multiplicity 3; , multiplicity 2E)
, multiplicity 2; , multiplicity 2; , multiplicity 1 Question
Determine the vertex of the graph of the quadratic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Describe the right-hand and the left-hand behavior of the graph of 
.
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
Determine the x-intercept(s) of the quadratic function 
.
A)
B)
C)
D)
E)no x-intercept(s)
.A)
B)
C)
D)
E)no x-intercept(s)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Using a graphing utility, graph 
and approximate the zeros and their multiplicity.
A)
, multiplicity 1; 
, multiplicity 2
B)
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1
C)
, multiplicity 2; 
, multiplicity 1
D)
, multiplicity 3
E)
, multiplicity 2; 
, multiplicity 1
and approximate the zeros and their multiplicity.A)
, multiplicity 1; , multiplicity 2B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 3E)
, multiplicity 2; , multiplicity 1 Question
Write the standard form of the equation of the parabola that has a vertex at 
and passes through the point 
.
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
Question
Find all real zeros of the polynomial 
and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1; , multiplicity 1B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
in the form 
when 
.
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
Question
Find all real zeros of the polynomial 
and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 1; , multiplicity 1; , multiplicity 1E)
, multiplicity 3 Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
in the form 
when 
.
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If 
, use synthetic division to evaluate 
.
A)
B)
C)
D)
E)
, use synthetic division to evaluate .A)
B)
C)
D)
E)
Question
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all real zeros of the polynomial 
and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 2B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the zero or root feature of a graphing utility to approximate the zeros of 
accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Question
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Use the quadratic formula to solve 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Write the complex conjugate of the complex number 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
Question
Combine 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Write the complex number 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
Question
Find real numbers a and b such that the equation 
is true.
A)
B)
C)
D)
E)
is true.A)
B)
C)
D)
E)
Question
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)The expression cannot be simplified.
and write the answer in standard form.A)
B)
C)
D)
E)The expression cannot be simplified.
Question
Combine 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find all the rational zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Question
Use the quadratic formula to solve 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
Question
Simplify: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Consider the function 
. Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
Question
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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: 
. Find the function's domain and identify any horizontal and vertical asymptotes.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
Use the zero or root feature of a graphing utility to approximate the zeros of the function 
accurate to the nearest thousandth.
A)
, 2.646, 2.449
B)
, -2.646, -2.449
C)
, 
2.646, 
2.449
D)2.646, 2.449
E)
, - 2.646, 2.449
accurate to the nearest thousandth.A)
, 2.646, 2.449B)
, -2.646, -2.449C)
, 2.646, 2.449D)2.646, 2.449
E)
, - 2.646, 2.449 Question
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Given 
is a root, determine all other roots of 
.
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
Question
Consider the function 
. Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
Question
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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: 
. Find the function's domain and identify any horizontal and vertical asymptotes.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
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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: 
. Find the function's domain and identify any horizontal and vertical asymptotes.A)domain: all real numbers; vertical asymptote:
; horizontal asymptote: noneB)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
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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: 
. Find the function's domain and identify any horizontal and vertical asymptotes.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
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Question
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Given 
is a root, determine all other roots of 
.
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
Question
Identify the function whose graph is provided. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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: 
. Find the function's domain and identify any horizontal and vertical asymptotes.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
Consider the function 
. Find the function's domain and identify any horizontal and vertical asymptotes.
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
. Find the function's domain and identify any horizontal and vertical asymptotes.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: noneD)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
Find the zeros (if any) of the rational function 
.
A)
B)
C)
and 
D)
E)There are no zeros.
.A)
B)
C)
and D)
E)There are no zeros.
Question
For the function given below, determine the domain, the x-intercepts, and any vertical and horizontal asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Question
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. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the zeros (if any) of the rational function 
.
A)
and 
B)
C)
D)
E)There are no zeros.
.A)
and B)
C)
D)
E)There are no zeros.
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Deck 3: Polynomial and Rational Functions
1
From the graph of the quadratic function , determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
2
Write the quadratic function, , in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
3
From the graph of the quadratic function , determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
4
Find the standard form of the quadratic function shown below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Find two positive real numbers whose product is a maximum and whose sum is .
A)
B)
C)
D)
E)58, 82
.A)
B)
C)
D)
E)58, 82
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6
Write the standard form of the equation of the parabola that has a vertex at and passes through the point .
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
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7
Write the quadratic function, , in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
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8
Determine the x-intercept(s) of the quadratic function .
A)
B)
C)
D)
E)no x-intercept(s)
.A)
B)
C)
D)
E)no x-intercept(s)
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9
Describe the right-hand and the left-hand behavior of the graph of .
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.
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10
Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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11
Compare the graph of with .
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 .
with .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 . Unlock Deck
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12
Describe the right-hand and the left-hand behavior of the graph of .
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.
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13
Using a graphing utility, graph and approximate the zeros and their multiplicity.
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
and approximate the zeros and their multiplicity.A)
, multiplicity 2; , multiplicity 3B)
, multiplicity 2; , multiplicity 1; , multiplicity 2C)
, multiplicity 3; , multiplicity 2D)
, multiplicity 3; , multiplicity 2E)
, multiplicity 2; , multiplicity 2; , multiplicity 1 Unlock Deck
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14
Determine the vertex of the graph of the quadratic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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15
Describe the right-hand and the left-hand behavior of the graph of .
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.
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16
Determine the x-intercept(s) of the quadratic function .
A)
B)
C)
D)
E)no x-intercept(s)
.A)
B)
C)
D)
E)no x-intercept(s)
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k this deck
17
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
18
Using a graphing utility, graph and approximate the zeros and their multiplicity.
A) , multiplicity 1; , multiplicity 2
B) , multiplicity 1; , multiplicity 1; , multiplicity 1
C) , multiplicity 2; , multiplicity 1
D) , multiplicity 3
E) , multiplicity 2; , multiplicity 1
and approximate the zeros and their multiplicity.A)
, multiplicity 1; , multiplicity 2B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 3E)
, multiplicity 2; , multiplicity 1 Unlock Deck
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19
Write the standard form of the equation of the parabola that has a vertex at and passes through the point .
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
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k this deck
20
Find all real zeros of the polynomial and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1; , multiplicity 1B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 Unlock Deck
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21
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
22
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Unlock Deck
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23
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
24
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
25
Write in the form when .
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
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k this deck
26
Find all real zeros of the polynomial and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 1; , multiplicity 1; , multiplicity 1E)
, multiplicity 3 Unlock Deck
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27
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
28
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Unlock Deck
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29
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
30
Write in the form when .
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
31
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
32
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
33
If , use synthetic division to evaluate .
A)
B)
C)
D)
E)
, use synthetic division to evaluate .A)
B)
C)
D)
E)
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34
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Unlock Deck
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35
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
36
Find all real zeros of the polynomial and determine the mutiplicity of each.
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
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 2B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 Unlock Deck
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37
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Unlock Deck
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38
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
39
Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
40
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Unlock Deck
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41
Find all real solutions of the polynomial equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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42
Use the quadratic formula to solve .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
43
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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44
Write the complex conjugate of the complex number .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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45
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
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46
Combine and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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47
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Unlock Deck
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48
Find all zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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49
Find all zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
50
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
51
Write the complex number in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
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52
Find real numbers a and b such that the equation is true.
A)
B)
C)
D)
E)
is true.A)
B)
C)
D)
E)
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53
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)The expression cannot be simplified.
and write the answer in standard form.A)
B)
C)
D)
E)The expression cannot be simplified.
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k this deck
54
Combine and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
55
Find all real solutions of the polynomial equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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56
Find all the rational zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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57
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
Unlock Deck
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58
Use the quadratic formula to solve .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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59
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
Unlock Deck
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60
Simplify:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
Consider the function . Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
Unlock Deck
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62
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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:
. Find the function's domain and identify any horizontal and vertical asymptotes.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: Unlock Deck
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63
Use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to the nearest thousandth.
A) , 2.646, 2.449
B) , -2.646, -2.449
C) , 2.646, 2.449
D)2.646, 2.449
E) , - 2.646, 2.449
accurate to the nearest thousandth.A)
, 2.646, 2.449B)
, -2.646, -2.449C)
, 2.646, 2.449D)2.646, 2.449
E)
, - 2.646, 2.449 Unlock Deck
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64
Find all the real zeros of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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65
Given is a root, determine all other roots of .
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
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66
Consider the function . Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
67
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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:
. Find the function's domain and identify any horizontal and vertical asymptotes.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: Unlock Deck
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68
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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:
. Find the function's domain and identify any horizontal and vertical asymptotes.A)domain: all real numbers; vertical asymptote:
; horizontal asymptote: noneB)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: Unlock Deck
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69
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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:
. Find the function's domain and identify any horizontal and vertical asymptotes.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: Unlock Deck
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70
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
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71
Find all the real zeros of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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72
Given is a root, determine all other roots of .
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
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Unlock for access to all 84 flashcards in this deck.
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73
Identify the function whose graph is provided.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
74
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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:
. Find the function's domain and identify any horizontal and vertical asymptotes.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: Unlock Deck
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k this deck
75
Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.
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
. Find the function's domain and identify any horizontal and vertical asymptotes.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: noneD)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 Unlock Deck
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76
Find the zeros (if any) of the rational function .
A)
B)
C) and
D)
E)There are no zeros.
.A)
B)
C)
and D)
E)There are no zeros.
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
77
For the function given below, determine the domain, the x-intercepts, and any vertical and horizontal asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
78
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
79
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.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
80
Find the zeros (if any) of the rational function .
A) and
B)
C)
D)
E)There are no zeros.
.A)
and B)
C)
D)
E)There are no zeros.
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
