AnswersNC-PrecalculusRational Inequalities

Graphing Exponential Functions Answers

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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of ?

Question illustration
A
A + StartFraction B Over x + 3 EndFraction + StartFraction C Over 2 x minus 7 EndFraction
Option A
B
A + StartFraction B x + C Over x + 3 EndFraction + StartFraction D x + E Over 2 x minus 7 EndFraction
Option B
C
A x + B + StartFraction C Over x + 3 EndFraction + StartFraction D Over 2 x minus 7 EndFraction
Option C
D
A x + B + StartFraction C x + D Over x + 3 EndFraction + StartFraction E x + F Over 2 x minus 7 EndFraction
Option D
3

Review the work showing the first few steps in writing a partial fraction decomposition.x3 + 8x – 3 = (Ax + B)(x2 + 5) + Cx + Dx3 + 8x – 3 = Ax3 + 5Ax + Bx2 + 5B + Cx + D

Question illustration
A
A = 0; B = 1; C = –3; D = 3
B
A = 0; B = 1; C = 3; D = –3
C
A = 1; B = 0; C = –3; D = 3
D
A = 1; B = 0; C = 3; D = –3
4

What is the solution to x 3 + 4x 2 > x + 4?

A
–4 < x < –1
B
–4 < x < 1
C
–4 1
D
x < –4 or –1 < x < 1
5

What is the solution of ?

Question illustration
A
or x > 4
Option A
B
or x > 4
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D
8

What is the solution of ?

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
9

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
10

What is the solution set of ?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
13

What is the correct form of the partial fraction decomposition for ?

Question illustration
A
StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction
Option A
B
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction
Option B
C
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction
Option C
D
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction
Option D
14

What is the solution to (x – 3)3(x + 1)(x – 2) ≤ 0?

A
(–ꝏ, –1) U (2, 3)
B
(–ꝏ, –1] U [2, 3]
C
(–1, 2) U (3, ꝏ)
D
[–1, 2] U [3, ꝏ)
15

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 1 Over 3 x EndFraction + StartFraction x minus 2 Over 4 x squared + 9 EndFraction
Option A
B
StartFraction 1 Over 3 x EndFraction + StartFraction x + 2 Over 4 x squared + 9 EndFraction
Option B
C
StartFraction negative 2 Over 3 x EndFraction + StartFraction x minus 1 Over 4 x squared + 9 EndFraction
Option C
D
StartFraction negative 2 Over 3 x EndFraction + StartFraction x + 1 Over 4 x squared + 9 EndFraction
Option D
17

What is the solution of ?

Question illustration
A
mc021-2.jpg
Option A
B
mc021-3.jpg
Option B
C
or
Option C
D
or
Option D
18

Review the work showing the first few steps in writing a partial fraction decomposition.4x + 40 = A(x + 6) + B(x + 2)4x + 40 = Ax + 6A + Bx + 2B

Question illustration
A
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 12 Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction
Option A
B
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 4 Over x + 2 EndFraction + StartFraction 8 Over x + 6 EndFraction
Option B
C
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction
Option C
D
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 16 Over x + 2 EndFraction + StartFraction negative 12 Over x + 6 EndFraction
Option D
19

What is the quotient and remainder, written as partial fractions, of ?

Question illustration
A
5 + StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option A
B
5 + StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option B
C
5 minus StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option C
D
5 minus StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option D
20

What is the correct form of the partial fraction decomposition for the expression ?

Question illustration
A
StartFraction A Over x squared + StartFraction B Over 9 x EndFraction
Option A
B
StartFraction A Over x EndFraction + StartFraction B Over x + 9 EndFraction
Option B
C
StartFraction A x + B Over x squared EndFraction + StartFraction C Over 9 x EndFraction
Option C
D
StartFraction A x + B Over x EndFraction + StartFraction C Over x + 9 EndFraction
Option D

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