AnswersPARTA - EVP PGCPS ALGEBRA 2 OC FALL2026 - 793033Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions — Unit test Answers

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1
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If the interval (a, ∞) describes all values of x for which the graph of is decreasing, what is the value of a?

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2
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Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction y + x Over y minus x EndFraction
Option A
B
StartFraction (y minus x) (y + x) Over x squared y squared EndFraction
Option B
C
StartFraction x squared y squared Over (y + x) (y + x) EndFraction
Option C
D
StartFraction y minus x Over y + x EndFraction
Option D
3

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

Question illustration
A
She added the two fractions incorrectly.
B
She used the wrong common denominator.
C
She did not distribute the negative correctly.
D
She did not multiply the first fraction by a factor.
4

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

A
Function 1 has a hole, while function 2 does not.
B
Function 1 has an oblique asymptote, while function 2 does not.
C
Function 2 has a hole, while function 1 only has asymptotes.
D
Function 2 only has asymptotes, while function 1 has a hole.
E
Both functions have the same domain restriction.
F
Both functions have the same vertical asymptote.
5

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

Question illustration
A
The oblique asymptote for g(x) is steeper than for f(x).
B
Both functions have the same oblique asymptote.
C
The oblique asymptote for f(x) is steeper than for g(x).
D
Both functions have parallel oblique asymptotes.
6

Which solution to the equation is extraneous?

Question illustration
A
a = –2
B
a = –2 and a = 4
C
neither a = –2 nor a = 4
D
a = 4
7

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it.Flow rate, x(gal/hr)Time, y(hours)60300454003650030600How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

A
100 hours
B
150 hours
C
180 hours
D
200 hours
8

A basketball player’s free-throw percentage is the ratio of the number of successful shots made to the number of shots attempted. A basketball player has made 13 of the first 20 free throws she has attempted this season. Which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free-throw attempts?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
10

Using V = lwh, what is an expression for the volume of the following rectangular prism?

Question illustration
A
StartFraction 15 Over 2 x EndFraction
Option A
B
StartFraction 3 x + 12 Over 2 x + 8 EndFraction
Option B
C
StartFraction 15 Over 2 x + 2 EndFraction
Option C
D
Fifteen-eighths
Option D
11

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction x minus 3 Over x EndFraction
Option A
B
StartFraction x + 3 Over 1 EndFraction
Option B
C
StartFraction x + 3 Over x EndFraction
Option C
D
StartFraction x Over x + 3 EndFraction
Option D
12

What is the solution to the equation ?

Question illustration
A
m = –4
B
m = –2
C
m = 2
D
m = 4
13

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

Question illustration
A
The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
B
The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
C
The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
D
The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
14

Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

A
2.0 mph
B
3.3 mph
C
5.0 mph
D
10.0 mph
15

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = negative 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = negative 2.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = 2.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1 , and the other curve opens down and to the left in quadrants 2, 1, and 4. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = 2.
Option D

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