Liberty University Algebra Worksheet

4/18/22, 4:09 PM1.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.2.015.
MY NOTES
ASK YOUR TEACHER
Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior.
P(x) = (x − 1)(x + 5)
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2.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.1.005.
MY NOTES
ASK YOUR TEACHER
The graph of a quadratic function f is given.
f(x) = −x2 + 4x − 3
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4/18/22, 4:09 PM
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
(a) Find the coordinates of the vertex and the x- and y-intercepts.
vertex
(x, y) =
x-intercepts
(x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
y-intercept
(x, y) =
(b) Find the maximum or minimum value of f.
The —Select—
value of f is f(x) =
.
(c) Find the domain and range of f. (Enter your answers using interval notation.)
domain
range
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3.
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
[–/2 Points]
DETAILS
SCOLALG7 3.6.024.MI.
MY NOTES
ASK YOUR TEACHER
Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.)
r(x) =
7
x2 + 3x − 8
(x, y) =
x-intercept
(x, y) =
y-intercept
4.
[–/2 Points]
DETAILS
SCOLALG7 3.1.035.
MY NOTES
ASK YOUR TEACHER
MY NOTES
ASK YOUR TEACHER
Find the maximum or minimum value of the function.
f(x) = 2×2 + 12x − 3
Is this a maximum or minimum value?
maximum value
minimum value
5.
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DETAILS
SCOLALG7 3.7.055.
In the vicinity of a bonfire the temperature T (in °C) at a distance of x meters from the center of the fire is given by
T(x) =
500,000
x2 + 400
.
At what range distances from the fire’s center is the temperature less than 260°C? (Assume x is positive. Round your values to one decimal
place. Enter your answer using interval notation.)
m
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Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.5.034.MI.
MY NOTES
ASK YOUR TEACHER
Factor the polynomial completely.
P(x) = x5 + 3×3
P(x) =
Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered
smallest to largest real part, then smallest to largest imaginary part.)
7.
x
=
with multiplicity
x
=
with multiplicity
x
=
with multiplicity
[–/2 Points]
DETAILS
SCOLALG7 3.3.053.MI.
MY NOTES
ASK YOUR TEACHER
Use the Factor Theorem to show if x − c is a factor of P(x) for the given value of c.
P(x) = x3 − 3×2 + 3x − 9,
x−3
Select
c=3
a factor of P(x).
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6/19
4/18/22, 4:09 PM
8.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.6.071.MI.
MY NOTES
ASK YOUR TEACHER
Find the slant asymptote and the vertical asymptote. (If an answer does not exist, enter DNE.)
2
r(x) = x − 7x − 8
x
slant asymptote
vertical asymptote
Sketch a graph of the function.
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7/19
4/18/22, 4:09 PM
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
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8/19
4/18/22, 4:09 PM
[–/2 Points]
9.
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.4.011.
MY NOTES
ASK YOUR TEACHER
A polynomial function P and its graph are given.
P(x) = 2×3 − x2 − 2x + 1
(a) List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.)
x=
(b) From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a commaseparated list. Enter all answers including repetitions.)
x=
10.
[–/2 Points]
DETAILS
SCOLALG7 3.4.005.MI.
MY NOTES
ASK YOUR TEACHER
List all possible rational zeros given by the Rational Zeros Theorem (but don’t check to see which actually are zeros). (Enter your answers as
a comma-separated list.)
P(x) = x3 − 2×2 + 2
x=
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9/19
4/18/22, 4:09 PM
11.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.3.033.MI.
MY NOTES
ASK YOUR TEACHER
Find the quotient and remainder using synthetic division.
x5 + 2×3 − 11
x−1
quotient
remainder
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10/19
4/18/22, 4:09 PM
12.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.2.037.MI.
MY NOTES
ASK YOUR TEACHER
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers
including repetitions.)
x=
P(x) = x3 + 3×2 − 9x − 27
Sketch the graph.
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13.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.3.025.MI.
MY NOTES
ASK YOUR TEACHER
Find the quotient and remainder using synthetic division.
2×2 − 7x + 1
x−4
quotient
remainder
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12/19
4/18/22, 4:09 PM
14.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.6.027.
MY NOTES
ASK YOUR TEACHER
From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter
your asymptotes as a comma-separated list of equations if necessary.)
x-intercept
(x, y) =
y-intercept
(x, y) =
vertical asymptote
horizontal asymptote
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13/19
4/18/22, 4:09 PM
15.
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
[–/2 Points]
DETAILS
SCOLALG7 3.6.009.
MY NOTES
ASK YOUR TEACHER
A rational function is given.
r(x) =
x
x−5
(a) Complete each table for the function. (Round your answers to three decimal places where applicable.)
Table 1
x
Table 2
r(x)
x
4.5
5.5
4.9
5.1
4.99
5.01
4.999
5.001
Table 3
x
r(x)
Table 4
r(x)
x
10
−10
50
−50
100
−100
1000
−1000
r(x)
(b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2.
r(x) →
as x → 5−
r(x) →
and as x → 5+.
(c) Determine the horizontal asymptote, based on Tables 3 and 4.
y=
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14/19
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16.
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.5.007.MI.
MY NOTES
ASK YOUR TEACHER
A polynomial P is given.
P(x) = x4 + 25×2
(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
x=
(b) Factor P completely.
P(x) =
[–/2 Points]
17.
DETAILS
SCOLALG7 3.5.031.MI.
MY NOTES
ASK YOUR TEACHER
Factor the polynomial completely.
Q(x) = x4 + 32×2 + 256
Q(x) =
Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered
smallest to largest real part, then smallest to largest imaginary part.)
x
=
with multiplicity
x
=
with multiplicity
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15/19
4/18/22, 4:09 PM
18.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.5.065.MI.
MY NOTES
ASK YOUR TEACHER
MY NOTES
ASK YOUR TEACHER
A polynomial P is given.
P(x) = x3 − 2×2 + 9x − 18
(a) Factor P into linear and irreducible quadratic factors with real coefficients.
P(x) =
(b) Factor P completely into linear factors with complex coefficients.
P(x) =
19.
[–/2 Points]
DETAILS
SCOLALG7 3.4.047.MI.
Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example 3(a). (Enter your answers as a commaseparated list. Enter all answers including repetitions.)
P(x) = x4 − 6×3 + 3×2 + 18x + 8
x=
20.
[–/2 Points]
DETAILS
SCOLALG7 3.7.005.
MY NOTES
ASK YOUR TEACHER
Solve the inequality. (Enter your answer using interval notation.)
(x + 8)2(x + 5)(x − 1) > 0
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16/19
4/18/22, 4:09 PM
21.
[–/2 Points]
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.1.039.
MY NOTES
ASK YOUR TEACHER
Find the maximum or minimum value of the function. (Round your answer to two decimal places.)
f(s) = s2 − 1.2s + 14
Is this a maximum or minimum value?
maximum value
minimum value
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17/19
4/18/22, 4:09 PM
22.
Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
[–/2 Points]
DETAILS
SCOLALG7 3.2.027.
MY NOTES
ASK YOUR TEACHER
Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior.
P(x) =
23.
1
(x + 2)2(x − 5)2
12
[–/2 Points]
DETAILS
SCOLALG7 3.1.051.MI.
MY NOTES
ASK YOUR TEACHER
If a ball is thrown directly upward with a velocity of 22 ft/s, its height (in feet) after t seconds is given by y = 22t − 16t2. What is the maximum
height attained by the ball? (Round your answer to the nearest whole number.)
ft
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24.
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Quiz: MQ Polynomial and Rational Functions – MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
DETAILS
SCOLALG7 3.7.042.
MY NOTES
ASK YOUR TEACHER
MY NOTES
ASK YOUR TEACHER
Find the domain of the given function. (Enter your answer using interval notation.)
g(x) =
25.
[–/2 Points]
4+x
4−x
DETAILS
SCOLALG7 3.7.009.
Solve the inequality. (Enter your answer using interval notation.)
6×3 − x2 < 9 − 54x Submit Assignment Home Save Assignment Progress My Assignments Request Extension Copyright © 1998 - 2022 Cengage Learning, Inc. All Rights Reserved TERMS OF USE PRIVACY https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982964#question3238820_43 19/19