AnswersPrecalculusModeling with Rational and Piecewise-Defined Functions: Part One

Modeling with Rational and Piecewise-Defined Functions: Part One — Test Answers

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1
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Which is a potential rational root of f of x at point cap p ?

A
The root at point cap p may be 5 thirds .
B
The root at point cap p may be 1 fifth .
C
The root at point cap p may be 1 third .
D
The root at point cap p may be 3 fifths .
2
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What are the values of cap A , cap b , cap c , and cap d ?

A
cap A is equal to 0 ; cap b is equal to 1 ; cap c is equal to negative 3 ; cap d is equal to 3
B
cap A is equal to 1 ; cap b is equal to 0 ; cap c is equal to negative 3 ; cap d is equal to 3
C
cap A is equal to 0 ; cap b is equal to 1 ; cap c is equal to 3 ; cap d is equal to negative 3
D
cap A is equal to 1 ; cap b is equal to 0 ; cap c is equal to 3 ; cap d is equal to negative 3
3

If f of negative 2 is equal to 0 , what are all the factors of the function f of x is equal to x cubed minus 2 x squared minus 68 x minus 120 ? Use the Remainder Theorem.

A
open paren x plus 2 close paren times open paren x plus 60 close paren
B
open paren x minus 10 close paren times open paren x plus 2 close paren times open paren x plus 6 close paren
C
open paren x plus 10 close paren times open paren x minus 2 close paren times open paren x minus 6 close paren
D
open paren x minus 2 close paren times open paren x minus 60 close paren
4

Marshall bought 32 ounces of mixed nuts, which are estimated to be 30 percent peanuts. Which expression can be used to find the percentage of peanut concentration of the final mix if he adds x ounces of peanuts?

A
y is equal to the fraction with numerator 0 point 3 repeating 32 plus 0 point 3 x and denominator 32 plus x times 100
B
y is equal to the fraction with numerator 0 point 3 repeating 32 plus x and denominator 32 plus x times 100
C
y is equal to the fraction with numerator 0 point 3 repeating 32 plus 0 point 3 x and denominator 32 times 100
D
y is equal to the fraction with numerator 0 point 3 repeating 32 plus x and denominator 32 times 100
5

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 m to the 4th 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 8 m to the 7th power n to the 6th power and denominator 3
D
the fraction with numerator 10 m to the 7th power n to the 6th power and denominator 3
9

Which expression is equivalent to the fraction with numerator 3 x to the negative 6 power y to the negative 3 power and denominator 15 x squared y to the 10th power ? Assume x is not equal to 0 , y is not equal to 0

A
the fraction with numerator y to the 7th power and denominator 5 x to the 4th power
B
the fraction with numerator 1 and denominator 5 x to the 8th power y to the 13th power
C
the fraction with numerator 5 and denominator x to the 4th power y to the 7th power
D
the fraction with numerator 5 and denominator x to the 12th power y to the 30th power
10

Which statement is true about the discontinuities of the function f of x ? f of x is equal to the fraction with numerator x plus 1 and denominator 6 x squared minus 7 x minus 3

A
There are holes at x is equal to negative 3 halves and x is equal to 1 third .
B
There are asymptotes at x is equal to negative 3 halves and x is equal to 1 third .
C
There are asymptotes at x is equal to 3 halves and x is equal to negative 1 third .
D
There are holes at x is equal to 3 halves and x is equal to negative 1 third .
11

What is the correct form of the partial fraction decomposition for the fraction with numerator 6 x plus 7 and denominator open paren x plus 2 close paren squared ?

A
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b and denominator open paren x plus 2 close paren squared
B
cap A over x plus the fraction with numerator cap b and denominator x plus 2 plus the fraction with numerator cap c x plus cap d and denominator open paren x plus 2 close paren squared
C
cap A over x plus the fraction with numerator cap b and denominator x plus 2 plus the fraction with numerator cap c and denominator open paren x plus 2 close paren squared
D
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 2 close paren squared
12

Using cap v is equal to l w h , what is an expression for the volume of the following prism? Expand Image

A
the fraction with numerator 1 and denominator 3 d minus 3
B
the fraction with numerator 4 d minus 8 and denominator 3 times open paren d minus 4 close paren squared
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 and denominator 3 d minus 12
17

f of x is equal to the fraction with numerator negative 2 x squared plus 14 and denominator x squared minus 49 Which statement describes the behavior of the graph of the function shown at the vertical asymptotes?

A
As x approaches negative 7 from the left, y approaches infinity .
B
As x approaches negative 7 from the right, y approaches negative infinity .
C
As x approaches 7 from the left, y approaches negative infinity .
D
As x approaches 7 from the right, y approaches negative infinity .
18

Use synthetic division to solve open paren x to the 4th power minus 1 close paren divided by open paren x minus 1 close paren What is the quotient?

A
x cubed minus 2
B
x cubed minus x squared plus x minus 1
C
x cubed
D
x cubed plus x squared plus x plus 1
19

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 m plus 4 and denominator open paren m minus 4 close paren times open paren m plus 2 close paren
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 open paren m minus 4 close paren times open paren m plus 2 close paren and denominator m plus 4

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