Graphing Rational Functions Answers

1

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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.

2

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What are the vertical and horizontal asymptotes for the function ?

A

horizontal asymptote: y = –2, y = 2vertical asymptote: x = 3

B

horizontal asymptote: y = –4, y = 1vertical asymptote: x = 3

C

horizontal asymptote: y = 3vertical asymptote: x = –4, x = 1

D

horizontal asymptote: y = 3vertical asymptote: x = –2, x = 2

3

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.

4

What is the horizontal asymptote of the function ?

A

y = 0

B

y = 1

C

y = 2

D

y = 3

5

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

6

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.

7

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

8

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

9

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.

10

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).

Graphing Rational Functions Answers

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