AnswersMathematics IIIRational Functions

Practice Test Answers

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1
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Which statement is true about the discontinuities of the function f of x ? f of x is equal to the fraction with numerator x squared minus 4 and denominator x cubed minus x squared minus 2 x

A
There is a hole at x is equal to 2 .
B
There are asymptotes at x is equal to 0 and x is equal to negative 1 .
C
There are asymptotes at x is equal to 0 and x is equal to negative 1 and a hole at open paren 2 comma 2 thirds close paren .
D
There are holes at x is equal to 0 and x is equal to negative 1 and an asymptote at x is equal to 2 .
2
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What is the product? the fraction with numerator 3 k and denominator k plus 1 times the fraction with numerator k squared minus 1 and denominator 3 k cubed

A
the fraction with numerator k minus 1 and denominator k squared
B
1 over k
C
negative 1 over k
D
the fraction with numerator k plus 1 and denominator k squared
4

Which solution to the equation the fraction with numerator 3 and denominator A plus 2 plus 2 over A is equal to the fraction with numerator 4 A minus 4 and denominator A squared minus 4 is extraneous?

A
A is equal to negative 2 and A is equal to 4
B
A is equal to 4
C
A is equal to negative 2
D
neither A is equal to negative 2 nor A is equal to 4
5

What is the quotient the fraction with numerator 2 m to the 9th power n to the 4th power and denominator negative 4 m to the negative 3 power n to the negative 2 power in simplest form? Assume m is not equal to 0 , n is not equal to 0

A
6 m to the 12th power n to the 6th power
B
negative the fraction with numerator m to the 27th power n to the 8th power and denominator 2
C
8 m to the 12th power n to the 6th power
D
negative the fraction with numerator m to the 12th power n to the 6th power and denominator 2
6

Which expression is equivalent to the following complex fraction? the fraction with numerator the fraction with numerator x and denominator x minus 3 and denominator the fraction with numerator x squared and denominator x squared minus 9

A
the fraction with numerator x and denominator x plus 3
B
the fraction with numerator x plus 3 and denominator 1
C
the fraction with numerator x minus 3 and denominator x
D
the fraction with numerator x plus 3 and denominator x
7

What is the quotient the fraction with numerator negative 8 A to the 8th power b to the negative 2 power and denominator 10 A to the negative 4 power b to the negative 10 power in simplified form? Assume A is not equal to 0 , b is not equal to 0

A
negative the fraction with numerator 4 A to the 12th power b to the 8th power and denominator 5
B
negative the fraction with numerator 4 A to the 32th power b to the 5th power and denominator 5
C
the fraction with numerator A to the 12th power b to the 8th power and denominator 80
D
the fraction with numerator A to the 32th power b to the 5th power and denominator 80
9

Naomi wants to take yoga classes. She can take classes at the high school for a one-time fee of 20 dollars plus 10 dollars per class. She can join the local gym for 50 dollars and take classes for 5 dollars per class. Which statement is true about the average cost for the two options?

A
The high school option costs less per class for six classes.
B
The high school option costs less per class for seven classes.
C
The gym option costs less per class for seven classes.
D
The gym option costs less per class for six classes.
10

What is the quotient? the fraction with numerator 3 y plus 2 and denominator 3 y divided by the fraction with numerator 6 y squared plus 4 y and denominator 3 y plus 2

A
the fraction with numerator 2 times open paren 3 y plus 2 close paren and denominator 3
B
1 over y
C
the fraction with numerator 3 y plus 2 and denominator 6 y squared
D
1 over 2 y
12

What are the vertical and horizontal asymptotes for the function f of x is equal to the fraction with numerator x squared plus x minus 6 and denominator x cubed minus 1 ?

A
vertical asymptote: x is equal to negative 2 , x is equal to 3 horizontal asymptote: y is equal to 0
B
vertical asymptote: x is equal to 1 horizontal asymptote: y is equal to 0
C
vertical asymptote: x is equal to 1 horizontal asymptote: none
D
vertical asymptote: x is equal to negative 2 , x is equal to negative 3 horizontal asymptote: none
13

For what values of A and m does f of x have a horizontal asymptote at y is equal to 2 and a vertical asymptote at x is equal to 1 ? f of x is equal to the fraction with numerator 2 x to the m th power and denominator x plus A

A
A is equal to negative 1 , m is equal to 1
B
A is equal to negative 1 , m is equal to 0
C
A is equal to 1 , m is equal to 0
D
A is equal to 1 , m is equal to 1

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