Graphing Rational Functions Answers

Which graph represents the function ?

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.

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.

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.

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.

2

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What is the domain of the function ?

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

3

Which statement describes the domain of the function ?

A

all real numbers

B

all nonzero real numbers

C

all real numbers except x =

D

all real numbers except x = –1 and x = 1

4

Which graph represents the function ?

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.

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.

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.

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.

5

Which graph represents the function ?

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.

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.

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.

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.

6

What is the domain of ?

A

all real numbers

B

all nonzero numbers

C

all real numbers except 1

D

all real numbers except 3

7

Which statement describes the behavior of the function ?

A

The graph approaches –3 as x approaches infinity.

B

The graph approaches 0 as x approaches infinity.

C

The graph approaches 3 as x approaches infinity.

D

The graph approaches 4 as x approaches infinity.

8

What is the horizontal asymptote of ?

A

y = –2

B

y = –1

C

y = 0

D

y = 1

9

What are the vertical and horizontal asymptotes of ?

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

10

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

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

11

Which function has no horizontal asymptote?

A

f (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction

B

f (x) = StartFraction x minus 1 Over 3 x EndFraction

C

f (x) = StartFraction 2 x squared Over 3 x minus 1 EndFraction

D

f (x) = StartFraction 3 x squared Over x squared minus 1 EndFraction

12

Which statement describes the behavior of the function ?

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.

13

How does the graph of compare to the graph of the parent function ?

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).

14

What is the horizontal asymptote of the function ?

A

y = 0

B

y = 1

C

y = 2

D

y = 3

15

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

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

Graphing Rational Functions Answers

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