AnswersTrigonometryPre-calculusGraphs of Rational Functions

Graphs of Rational Functions — Quiz Answers

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1
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Which equation models the rational function shown in the graph?

A
f of x is equal to the fraction with numerator x minus 2 and denominator x plus 2
B
f of x is equal to the fraction with numerator x plus 2 and denominator x minus 2
C
f of x is equal to the fraction with numerator 2 times open paren x minus 2 close paren and denominator x plus 2
D
f of x is equal to the fraction with numerator 2 times open paren x plus 2 close paren and denominator x minus 2
2
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The graph of f of x is equal to the fraction with numerator 24 x squared plus 62 x plus 34 and denominator 4 x plus 3 has an oblique asymptote at y is equal to

A
62 x plus 34 .
B
4 x plus 3 .
C
x plus 1 .
D
6 x plus 11 .
3

f of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 6 times open paren x minus 4 close paren g of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 8 times open paren x minus 4 close paren Which statement comparing the oblique asymptotes of the functions f of x and g of x is true?

A
The oblique asymptote for g of x is steeper than for f of x .
B
The oblique asymptote for f of x is steeper than for g of x .
C
Both functions have the same oblique asymptote.
D
Both functions have parallel oblique asymptotes.
4

Consider the function f of x is equal to the fraction with numerator 9 minus x squared and denominator x squared minus 4 For which intervals is f of x positive? Choose two correct answers.

A
open paren negative 3 comma negative 2 close paren
B
open paren negative infinity comma negative 3 close paren
C
open paren infinity comma 3 close paren
D
open paren 2 comma 3 close paren
E
open paren negative 2 comma 2 close paren
5

f of x is equal to the fraction with numerator open paren x minus 2 close paren times open paren x plus 1 close paren and denominator x plus 1 Which statements describe the end behavior of the graph of the function shown? Choose two correct answers.

A
As x rightarrow negative infinity , y rightarrow infinity .
B
As x rightarrow infinity , y rightarrow 1 .
C
As x rightarrow negative infinity , y rightarrow 1 .
D
As x rightarrow infinity , y rightarrow negative infinity .
E
As x rightarrow negative infinity , y rightarrow negative infinity .
F
As x rightarrow infinity , y rightarrow infinity .
6

f of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 6 times open paren x minus 4 close paren g of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 8 times open paren x minus 4 close paren Which statement comparing the oblique asymptotes of the functions f of x and g of x is true?

A
Both functions have parallel oblique asymptotes.
B
The oblique asymptote for f of x is steeper than for g of x .
C
Both functions have the same oblique asymptote.
D
The oblique asymptote for g of x is steeper than for f of x .
7

At which values of x does the graph of f of x is equal to the fraction with numerator x squared minus x minus 2 and denominator open paren x squared minus 1 close paren times open paren x squared minus 16 close paren have a vertical asymptote? Choose three correct answers.

A
1
B
2
C
4
D
negative 4
E
negative 1
8

Consider the function f of x is equal to the fraction with numerator 9 minus x squared and denominator x squared minus 4 For which intervals is f of x positive? Choose two correct answers.

A
open paren negative 3 comma negative 2 close paren
B
open paren infinity comma 3 close paren
C
open paren 2 comma 3 close paren
D
open paren negative infinity comma negative 3 close paren
E
open paren negative 2 comma 2 close paren
9

Which function has a graph with a horizontal asymptote at y is equal to 3 , a vertical asymptote at x is equal to 1 , and an x -intercept at 2 ?

A
f of x is equal to the fraction with numerator x minus 1 and denominator 3 times open paren x minus 2 close paren
B
f of x is equal to the fraction with numerator x minus 2 and denominator 3 times open paren x minus 1 close paren
C
f of x is equal to the fraction with numerator 3 times open paren x minus 1 close paren and denominator x minus 2
D
f of x is equal to the fraction with numerator 3 times open paren x minus 2 close paren and denominator x minus 1
10

g of x is equal to the fraction with numerator negative 4 x squared plus 36 and denominator x plus 3 What key features does f of x , shown in the graph, share with g of x , shown in the equation? Choose three correct answers.

A
a vertical asymptote
B
an oblique asymptote
C
at least one y -intercept
D
at least one x -intercept
E
the domain of x

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