AnswersPrecalculusModeling with Rational and Piecewise-Defined Functions: Part One

Practice Test Answers

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If open paren x minus 5 close paren is a factor of f of x , which of the following must be true?

A
A root of f of x is x is equal to negative 5 .
B
A root of f of x is x is equal to 5 .
C
Both x is equal to negative 5 and x is equal to 5 are roots of f of x .
D
Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .
3

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 are asymptotes at x is equal to 0 and x is equal to negative 1 .
B
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 .
C
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 .
D
There is a hole at x is equal to 2 .
4

The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

A
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
B
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
C
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
D
plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
5

What is the correct form of the partial fraction decomposition for the fraction with numerator 35 minus 27 x and denominator 4 x squared plus 28 x ?

A
the fraction with numerator cap A x plus cap b and denominator 4 x squared plus cap c over 28 x
B
the fraction with numerator cap A and denominator 4 x squared plus cap b over 28 x
C
cap A over 4 x plus the fraction with numerator cap b and denominator x plus 7
D
the fraction with numerator cap A x plus cap b and denominator 4 x plus the fraction with numerator cap c and denominator x plus 7
7

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 negative 2
C
neither A is equal to negative 2 nor A is equal to 4
D
A is equal to 4
9

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
negative 1 over k
B
1 over k
C
the fraction with numerator k minus 1 and denominator k squared
D
the fraction with numerator k plus 1 and denominator k squared
10

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
neither A is equal to negative 2 nor A is equal to 4
B
A is equal to negative 2
C
A is equal to negative 2 and A is equal to 4
D
A is equal to 4
11

What is the quotient of open paren 2 x to the 4th power minus 3 x cubed minus 3 x squared plus 7 x minus 3 close paren divided by open paren x squared minus 2 x plus 1 close paren ?

A
2 x squared plus x minus 3 minus the fraction with numerator 6 and denominator x squared minus 2 x plus 1
B
2 x squared plus x minus 3
C
2 x squared minus x
D
2 x to the 4th power minus 3 x cubed minus 11 halves
12

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
1 over y
B
the fraction with numerator 2 times open paren 3 y plus 2 close paren and denominator 3
C
1 over 2 y
D
the fraction with numerator 3 y plus 2 and denominator 6 y squared
13

For the fraction with numerator 8 x to the 7th power plus 10 x to the 6th power plus 20 x to the 5th power plus 33 x to the 4th power plus 23 x cubed plus 37 x squared plus 9 x plus 4 and denominator open paren x plus 1 close paren squared times open paren x squared plus 1 close paren cubed , which expression represents the correct form of the partial fraction decomposition?

A
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c and denominator open paren x plus 1 close paren cubed plus the fraction with numerator cap d x plus cap e and denominator x squared plus 1 plus the fraction with numerator cap f x plus cap g and denominator open paren x squared plus 1 close paren squared
B
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b squared and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c cubed and denominator open paren x plus 1 close paren cubed plus the fraction with numerator cap d x plus cap e and denominator x squared plus 1 plus the fraction with numerator open paren cap f x plus cap g close paren squared and denominator open paren x squared plus 1 close paren squared
C
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b squared and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c x plus cap d and denominator x squared plus 1 plus the fraction with numerator open paren cap e x plus cap f close paren squared and denominator open paren x squared plus 1 close paren squared plus the fraction with numerator open paren cap g x plus cap h close paren cubed and denominator open paren x squared plus 1 close paren cubed
D
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c x plus cap d and denominator x squared plus 1 plus the fraction with numerator cap e x plus cap f and denominator open paren x squared plus 1 close paren squared plus the fraction with numerator cap g x plus cap h and denominator open paren x squared plus 1 close paren cubed
15

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
8 m to the 12th power n to the 6th power
B
6 m to the 12th power n to the 6th power
C
negative the fraction with numerator m to the 27th power n to the 8th power and denominator 2
D
negative the fraction with numerator m to the 12th power n to the 6th power and denominator 2
16

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 gym option costs less per class for seven classes.
B
The high school option costs less per class for six classes.
C
The gym option costs less per class for six classes.
D
The high school option costs less per class for seven classes.
17

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
the fraction with numerator A to the 32th power b to the 5th power and denominator 80
B
the fraction with numerator A to the 12th power b to the 8th power and denominator 80
C
negative the fraction with numerator 4 A to the 32th power b to the 5th power and denominator 5
D
negative the fraction with numerator 4 A to the 12th power b to the 8th power and denominator 5
18

What is the correct form of the partial fraction decomposition for the fraction with numerator 35 minus 27 x and denominator 4 x squared plus 28 x ?

A
the fraction with numerator cap A and denominator 4 x squared plus cap b over 28 x
B
the fraction with numerator cap A x plus cap b and denominator 4 x squared plus cap c over 28 x
C
the fraction with numerator cap A x plus cap b and denominator 4 x plus the fraction with numerator cap c and denominator x plus 7
D
cap A over 4 x plus the fraction with numerator cap b and denominator x plus 7
19

Which statements comparing the graphs of function 1 and function 2 are true? Choose three correct answers.

A
Function 2 only has asymptotes, while function 1 has a hole.
B
Function 1 has an oblique asymptote, while function 2 does not.
C
Function 1 has a hole, while function 2 does not.
D
Function 2 has a hole, while function 1 only has asymptotes.
E
Both functions have the same domain restriction.
F
Both functions have the same vertical asymptote.
20

Identify the horizontal and vertical asymptotes, if any, for the graph of f of x shown. Choose two correct answers.

A
y is equal to 0
B
x is equal to 1
C
y is equal to 1
D
no vertical asymptotes
E
no horizontal asymptotes
F
x is equal to negative 1

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