AnswersTX-Algebra II B-CRUnit Test

Graphing Rational Functions Answers

6 verified answers
1
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How does the graph of compare to the graph of the parent function ?

Question illustration
A
g(x) is shifted 5 units left and 2 units up from f(x).
B
g(x) is shifted 5 units right and 2 units up from f(x).
C
g(x) is shifted 5 units left and 2 units down from f(x).
D
g(x) is shifted 5 units right and 2 units down from f(x).
2
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What is the horizontal asymptote of the function ?

Question illustration
A
y = 0
B
y = 1
C
y = 2
D
y = 3
3

What is the domain of the function ?

Question illustration
A
all real numbers
B
all real numbers except –1
C
all real numbers except –4 and –2
D
all real numbers except 2 and 4
4

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Option D
5

What is the horizontal asymptote of ?

Question illustration
y
y = –2
y
y = –1
y
y = 0
y
y = 1
6

What are the equations of the asymptotes of the graph of the function ?

Question illustration
A
x = –5, x = 2 and y = 3
B
x = –2, x = 5 and y = 3
C
x = 3, y = –5, and y = 2
D
x = 3, y = –2, and y = 5
7

Which statement describes the domain of the function ?

Question illustration
A
all real numbers
B
all nonzero real numbers
C
all real numbers except x =
Option C
D
all real numbers except x = –1 and x = 1
8

What are the vertical and horizontal asymptotes of ?

Question illustration
A
horizontal asymptote at y = 0, vertical asymptote at x = 1
B
horizontal asymptote at y = 2, vertical asymptote at x = 1
C
horizontal asymptote at y = 1, vertical asymptote at x = 0
D
horizontal asymptote at y = 1, vertical asymptote at x = 2
9

Which statement describes the behavior of the function ?

Question illustration
A
The graph approaches –2 as x approaches infinity.
B
The graph approaches 0 as x approaches infinity.
C
The graph approaches 1 as x approaches infinity.
D
The graph approaches 2 as x approaches infinity.
10

How does the range of compare with the range of the parent function ?

Question illustration
A
The range of both f(x) and g(x) is all real numbers
B
The range of both f(x) and g(x) is all nonzero real numbers
C
The range of f(x) is all real numbers, the range of g(x) is all real numbers except 6
D
The range of f(x) is all nonzero real numbers, the range of g(x) is all real numbers except 6
11

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = 1.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 0.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1.
Option D
12

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
Option D
13

Which function has no horizontal asymptote?

A
f (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction
Option A
B
f (x) = StartFraction x minus 1 Over 3 x EndFraction
Option B
C
f (x) = StartFraction 2 x squared Over 3 x minus 1 EndFraction
Option C
D
f (x) = StartFraction 3 x squared Over x squared minus 1 EndFraction
Option D

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