AnswersPrecalculusModeling with Rational and Piecewise-Defined Functions: Part Two

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

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What is the domain of the graphed function?

A
open paren negative infinity comma 4 close paren
B
left bracket negative 2 comma 0 right bracket and open paren 7 comma infinity close paren
C
open paren negative 2 comma infinity close paren
D
left parenthesis negative 2 comma 4 right bracket and left bracket 7 comma infinity right parenthesis
22
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Which statement correctly explains whether tis limit exists? limit x to 3 of g times x

A
The limits limit x to 3 raised to the negative power of g times x is equal to negative 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to 1 point 6 . Both limit x to 3 raised to the negative power of g times x and limit x to 3 raised to the plus power of g times x exist, so​​​​ limit x to 3 of g times x exists.
B
The limits limit x to 3 raised to the negative power of g times x is equal to negative 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to 1 point 6 . Because limit x to 3 raised to the negative power of g times x is not equal to limit x to 3 raised to the plus power of g times x , limit x to 3 to the th power of g times x does not exist.
C
The limits limit x to 3 raised to the negative power of g times x is equal to 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to negative 1 point 6 . Because limit x to 3 raised to the negative power of g times x is not equal to limit x to 3 raised to the plus power of g times x , limit x to 3 to the th power of g times x does not exist.
D
The limits limit x to 3 raised to the negative power of g times x is equal to 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to negative 1 point 6 . Both limit x to 3 raised to the negative power of g times x and limit x to 3 raised to the plus power of g times x exist, so limit x to 3 to the th power of g times x exists.
23

What is the vertex of the absolute value function?

A
open paren 1 comma negative 4 close paren
B
open paren 1 comma 4 close paren
C
open paren 4 comma 1 close paren
D
open paren 4 comma negative 1 close paren
24

Which statement describes the behavior of the function around the vertical asymptotes?

A
Around x is equal to negative 3 , limit x to negative 3 raised to the negative power of f times x is equal to negative infinity and limit x to negative 3 raised to the plus power of f times x is equal to infinity . Around x is equal to 3 , the function behaves in the same manner as around x is equal to negative 3 .
B
Around x is equal to negative 3 , limit x to negative 3 raised to the negative power of f times x is equal to infinity and limit x to negative 3 raised to the plus power of f times x is equal to negative infinity . Around x is equal to 3 , the function behaves in the opposite manner as around x is equal to negative 3 .
C
Around x is equal to negative 3 , limit x to negative 3 raised to the negative power of f times x is equal to negative infinity and limit x to negative 3 raised to the plus power of f times x is equal to infinity . Around x is equal to 3 , the function behaves in the opposite manner as around x is equal to negative 3 .
D
Around x is equal to negative 3 , limit x to negative 3 raised to the negative power of f times x is equal to infinity and limit x to negative 3 raised to the plus power of f times x is equal to negative infinity . Around x is equal to 3 , the function behaves in the same manner as around x is equal to negative 3 .
25

For which value of a does this limit not exist? limit x to A of g times x

A
negative 3
B
3
C
negative 6
D
0

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