AnswersCMS 2026-2027 NC Math 3 CREDIT RECOVERYRational Functions

Rational Functions — Test Answers

25 verified answers
1
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What is the quotient the fraction with numerator 15 p to the negative 4 power q to the negative 6 power and denominator negative 20 p to the negative 12 power q to the negative 3 power in simplified form? Assume p is not equal to 0 , q is not equal to 0

A
negative the fraction with numerator 3 and denominator 4 p to the 16th power q to the 9th power
B
negative the fraction with numerator 1 and denominator 5 p to the 16th power q to the 9th power
C
negative the fraction with numerator p to the 8th power and denominator 5 q cubed
D
negative the fraction with numerator 3 p to the 8th power and denominator 4 q cubed
2
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Which expression is equivalent to the fraction with numerator m minus 4 and denominator m plus 4 divided by open paren m plus 2 close paren ?

A
the fraction with numerator open paren m plus 4 close paren times open paren m plus 2 close paren and denominator m minus 4
B
the fraction with numerator open paren m minus 4 close paren times open paren m plus 2 close paren and denominator m plus 4
C
the fraction with numerator m minus 4 and denominator open paren m plus 4 close paren times open paren m plus 2 close paren
D
the fraction with numerator m plus 4 and denominator open paren m minus 4 close paren times open paren m plus 2 close paren
3

Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work? the fraction with numerator x and denominator x squared minus 1 minus the fraction with numerator 1 and denominator x minus 1 Knotts’s Work Step 1: the fraction with numerator x and denominator open paren x plus 1 close paren times open paren x minus 1 close paren minus the fraction with numerator 1 and denominator x minus 1 Step 2: the fraction with numerator x and denominator open paren x plus 1 close paren times open paren x minus 1 close paren minus the fraction with numerator 1 times open paren x plus 1 close paren and denominator open paren x plus 1 close paren times open paren x minus 1 close paren Step 3: the fraction with numerator x minus x plus 1 and denominator open paren x plus 1 close paren times open paren x minus 1 close paren Step 4: the fraction with numerator 1 and denominator open paren x plus 1 close paren times open paren x minus 1 close paren

A
In step 1, he did not correctly factor the denominator.
B
In step 4, he did not correctly subtract the numerator.
C
In step 3, he did not distribute the negative sign when he subtracted.
D
In step 2, he did not use the correct common denominator.
4

What is the product? the fraction with numerator 4 n and denominator 4 n minus 4 times the fraction with numerator n minus 1 and denominator n plus 1

A
the fraction with numerator n and denominator n plus 1
B
the fraction with numerator 4 and denominator n plus 1
C
the fraction with numerator 1 and denominator n plus 1
D
the fraction with numerator 4 n and denominator n plus 1
5

Which expression is equivalent to the fraction with numerator open paren 3 m to the negative 2 power n close paren to the negative 3 power and denominator 6 m n to the negative 2 power ? Assume m is not equal to 0 , n is not equal to 0

A
the fraction with numerator 4 m to the 8th power and denominator 3 n cubed
B
the fraction with numerator m to the 5th power and denominator 162 n
C
the fraction with numerator 8 m to the 9th power and denominator n to the 9th power
D
the fraction with numerator 1 and denominator 2 m cubed n
6

How can Ari simplify the following expression? the fraction with numerator the fraction with numerator 5 and denominator A minus 3 minus 4 and denominator 2 plus the fraction with numerator 1 and denominator A minus 3

A
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator.
B
Divide the numerator and the denominator by A minus 3 . Then divide the numerator by the denominator.
C
Divide the numerator and the denominator by A minus 3 . Then simplify the numerator and simplify the denominator.
D
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerators and multiply the denominators.
7

Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together. 1 over 45 plus 1 over 90 is equal to 1 over t How long will it take Maxine and Jan to mow the lawn together?

A
67 point 5 minutes
B
45 point 0 minutes
C
30 point 0 minutes
D
135 point 0 minutes
8

The increase in a person’s body temperature cap t times t , above 98.6 degrees F, can be modeled by the function cap t times t is equal to the fraction with numerator 4 t and denominator t squared plus 1 , where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?

A
The horizontal asymptote of y is equal to 4 means that the person’s temperature will approach 4 degrees F as time elapses.
B
The horizontal asymptote of y is equal to 0 means that the person’s temperature will approach 0 degrees F as time elapses.
C
The horizontal asymptote of y is equal to 4 means that the person’s temperature will approach 102.6 degrees F as time elapses.
D
The horizontal asymptote of y is equal to 0 means that the person’s temperature will approach 98.6 degrees F as time elapses.
9

What is the product? 6 times open paren x squared minus 1 close paren times the fraction with numerator 6 x minus 1 and denominator 6 times open paren x plus 1 close paren

A
open paren x plus 1 close paren times open paren 6 x minus 1 close paren
B
6 times open paren x minus 1 close paren squared
C
6 times open paren x squared minus 1 close paren
D
open paren x minus 1 close paren times open paren 6 x minus 1 close paren
10

Which expression is equivalent to the following complex fraction? the fraction with numerator negative 2 over x plus 5 over y and denominator 3 over y minus 2 over x

A
the fraction with numerator open paren negative 2 y plus 5 x close paren times open paren 3 x minus 2 y close paren and denominator x squared y squared
B
the fraction with numerator x squared y squared and denominator open paren negative 2 y plus 5 x close paren times open paren 3 x minus 2 y close paren
C
the fraction with numerator negative 2 y plus 5 x and denominator 3 x minus 2 y
D
the fraction with numerator 3 x minus 2 y and denominator negative 2 y plus 5 x
11

Which expression is equivalent to the fraction with numerator open paren 2 m n close paren to the 4th power and denominator 6 m to the negative 3 power n to the negative 2 power ? Assume m is not equal to 0 , n is not equal to 0

A
the fraction with numerator 10 m to the 7th power n to the 6th power and denominator 3
B
the fraction with numerator 8 m to the 16th power n to the 12th power and denominator 3
C
the fraction with numerator m to the 4th power n to the 6th power and denominator 3
D
the fraction with numerator 8 m to the 7th power n to the 6th power and denominator 3
12

What is the solution to the equation the fraction with numerator y and denominator y minus 4 minus the fraction with numerator 4 and denominator y plus 4 is equal to the fraction with numerator 32 and denominator y squared minus 16 ?

A
all real numbers
B
y is equal to 0
C
no solution
D
y is equal to negative 4 and y is equal to 4
13

Which expression is equivalent to open paren the fraction with numerator open paren 3 x y to the negative 5 power close paren cubed and denominator open paren x to the negative 2 power y squared close paren to the negative 4 power close paren to the negative 2 power ? Assume x is not equal to 0 , y is not equal to 0

A
the fraction with numerator x to the 22th power and denominator 18 y to the 46th power
B
the fraction with numerator 729 and denominator x to the 10th power y to the 14th power
C
the fraction with numerator 18 y to the 46th power and denominator x to the 22th power
D
the fraction with numerator x to the 10th power y to the 14th power and denominator 729
14

How does the graph of g of x is equal to the fraction with numerator 1 and denominator x plus 4 minus 6 compare to the graph of the parent function f of x is equal to 1 over x ?

A
g of x is shifted 4 units left and 6 units up from f of x .
B
g of x is shifted 4 units left and 6 units down from f of x .
C
g of x is shifted 4 units right and 6 units down from f of x .
D
g of x is shifted 4 units right and 6 units up from f of x .
15

How many extraneous solutions does the equation have? the fraction with numerator 2 m and denominator 2 m plus 3 minus the fraction with numerator 2 m and denominator 2 m minus 3 is equal to 1

A
0
B
1
C
2
D
3
16

Which expression is equivalent to the quotient? the fraction with numerator the fraction with numerator m plus 3 and denominator m squared minus 16 and denominator the fraction with numerator m squared minus 9 and denominator m plus 4

A
the fraction with numerator m plus 3 and denominator m plus 4
B
the fraction with numerator m minus 4 and denominator m minus 3
C
the fraction with numerator 1 and denominator open paren m minus 4 close paren times open paren m minus 3 close paren
D
the fraction with numerator 1 and denominator open paren m plus 4 close paren times open paren m plus 3 close paren
17

Which graph represents the function f of x is equal to the fraction with numerator 2 x and denominator x squared minus 1 ?

A
Image with description A coordinate plane with a graph showing three branches. The branch on the left approaches y equals 2 as x approaches negative infinity from the right and approaches infinity as x approaches negative 1 from the left. The branch in the middle approaches negative infinity as x approaches negative 1 from the right and approaches negative infinity as x approaches 1 from the left. The branch on the right approaches infinity as x approaches 1 from the right and approaches y equals 2 as x approaches infinity from the left.
B
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 2 as x approaches negative infinity from the right and approaches negative infinity as x approaches 1 from the left. The branch on the right approaches infinity as x approaches 1 from the right and approaches y equals 2 as x approaches infinity from the left.
C
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 1 as x approaches negative infinity from the right and approaches negative infinity as x approaches 0 from the left. The branch on the right approaches negative infinity as x approaches 1 from the right and approaches y equals 1 as x approaches infinity from the left.
D
Image with description A coordinate plane with a graph showing three branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. The branch in the middle approaches infinity as x approaches negative 1 from the right and approaches negative infinity as x approaches 1 from the left. It has a turning point at the origin. The branch on the right approaches infinity as x approaches 1 from the right and approaches the x-axis as x approaches infinity from the left.
18

Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the following equation, where t is the number of hours it would take to clear the field together. 1 third plus 1 half is equal to 1 over t How long will it take Ted and Jacob to clear the field together?

A
50 minutes
B
2 hours 30 minutes
C
12 minutes
D
1 hour 12 minutes
19

Using cap v is equal to l w h , what is an expression for the volume of the following prism? Open image in full-screen view

A
the fraction with numerator 1 and denominator 3 d minus 3
B
the fraction with numerator 4 and denominator 3 d minus 12
C
the fraction with numerator 4 times open paren d minus 2 close paren and denominator 3 open paren d minus 3 close paren open paren d minus 4 close paren
D
the fraction with numerator 4 d minus 8 and denominator 3 times open paren d minus 4 close paren squared
20

Which of the following represents the solution of 3 halves is equal to 3 over 2 x minus 6 over 5 x ?

A
x is equal to 1 fifth
B
x is equal to 5 ninths
C
all real numbers
D
no solution

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