AnswersPrecalculusModeling with Rational and Piecewise-Defined Functions: Part One

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

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21
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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of (8⁢x^3−2⁢x^2−67⁢x−24)/(2⁢x^2−x−21) ?

A
cap A plus the fraction with numerator cap b and denominator x plus 3 plus the fraction with numerator cap c and denominator 2 x minus 7
B
cap A plus the fraction with numerator cap b x plus cap c and denominator x plus 3 plus the fraction with numerator cap d x plus cap e and denominator 2 x minus 7
C
cap A x plus cap b plus the fraction with numerator cap c and denominator x plus 3 plus the fraction with numerator cap d and denominator 2 x minus 7
D
cap A x plus cap b plus the fraction with numerator cap c x plus cap d and denominator x plus 3 plus the fraction with numerator cap e x plus cap f and denominator 2 x minus 7
22
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According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 5 x cubed minus 7 x plus 11 ?

A
0 , plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
B
plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
C
plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
D
plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5
23

Which statement describes the vertical asymptotes of the graph of f of x is equal to the fraction with numerator x squared minus 64 and denominator 8 x minus 64 ?

A
The graph has no vertical asymptote.
B
The graph has a vertical asymptote at x is equal to 8 only.
C
The graph has a vertical asymptote at x is equal to negative 8 only.
D
The graph has vertical asymptotes at both x is equal to 8 and x is equal to negative 8 .

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