تكلم مع الذكاء الاصطناعي
Deck 3: Polynomial and Rational Functions
ملء الشاشة (f)
سؤال
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)
سؤال
Write the quadratic function, 
, in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Find the standard form of the quadratic function shown below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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
سؤال
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)
سؤال
Write the quadratic function, 
, in standard form.
A)
B)
C)
D)
E)
, in standard form.A)
B)
C)
D)
E)
سؤال
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)
سؤال
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.
سؤال
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)
سؤال
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 . سؤال
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.
سؤال
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 سؤال
Determine the vertex of the graph of the quadratic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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.
سؤال
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)
سؤال
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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 سؤال
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)
سؤال
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 سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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)
; سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write 
in the form 
when 
.
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
سؤال
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 سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write 
in the form 
when 
.
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
If 
, use synthetic division to evaluate 
.
A)
B)
C)
D)
E)
, use synthetic division to evaluate .A)
B)
C)
D)
E)
سؤال
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)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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 سؤال
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)
; سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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)
سؤال
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)
; سؤال
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the quadratic formula to solve 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Write the complex conjugate of the complex number 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
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)
سؤال
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)
سؤال
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Write the complex number 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
سؤال
Find real numbers a and b such that the equation 
is true.
A)
B)
C)
D)
E)
is true.A)
B)
C)
D)
E)
سؤال
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.
سؤال
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)
سؤال
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find all the rational zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Use the quadratic formula to solve 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Simplify: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Consider the function 
. Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
سؤال
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: سؤال
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 سؤال
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Consider the function 
. Identify any slant asymptotes.
A)
B)
C)
D)
E)
. Identify any slant asymptotes.A)
B)
C)
D)
E)
سؤال
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: سؤال
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: سؤال
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: سؤال
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
سؤال
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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)
سؤال
Identify the function whose graph is provided. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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: سؤال
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 سؤال
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.
سؤال
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)
سؤال
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
سؤال
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)
سؤال
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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العب
ملء الشاشة (f)
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 . فتح الحزمة
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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 فتح الحزمة
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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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17
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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 فتح الحزمة
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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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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 فتح الحزمة
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21
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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)
; فتح الحزمة
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23
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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25
Write in the form when .
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
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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 فتح الحزمة
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27
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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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)
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29
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Write in the form when .
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
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31
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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32
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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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)
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35
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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 فتح الحزمة
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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)
; فتح الحزمة
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38
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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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)
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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)
; فتح الحزمة
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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)
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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)
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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)
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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)
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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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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)
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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)
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58
Use the quadratic formula to solve .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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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)
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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)
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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: فتح الحزمة
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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 فتح الحزمة
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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)
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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: فتح الحزمة
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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: فتح الحزمة
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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: فتح الحزمة
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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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73
Identify the function whose graph is provided.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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: فتح الحزمة
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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 فتح الحزمة
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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.
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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)
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78
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
فتح الحزمة
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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)
فتح الحزمة
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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.
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