7/22/2019 8-3ws

1/2

Name Class Date

8-3Practice Form G

Find the domain, points of discontinuity, and x- and y-intercepts of each rationalfunction. Determine whether the discontinuities are removable or nonremovable.

1.( 4)( 3)

3

x xy

x

+=

+

2.( 3)( 1)

2

x xy

x

+

=

3.2

1y

x=

+

4.4

4

16

xy

x=

+

Find the vertical asymptotes and holes for the graph of each rational function.

5.2

5

1

xy

x

=

6.2 2

2

xy

x

=

+

7.( 1)

xy

x x=

8.2

3

9

xy

x

+=

9.2

( 2)( 2)

xy

x x

=

+

10.2

2

4

4

xy

x

=

+

11.2 25

4

xy

x

=

12.( 2)(2 3)

(5 4)( 3)

x xy

x x

+=

+

Find the horizontal asymptote of the graph of each rational function.

13.2

6y

x=

14.2

4

xy

x

+=

15.2

2

2 3

6

xy

x

+=

16.2

3 12

2

xy

x

=

Sketch the graph of each rational function.

17.3

2y

x=

18.3

( 2)( 2)y

x x=

+

19.2 4

xy

x=

+

20.2

1

xy

x

+=

Prentice Hall Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.

23

Rational Functions and Their Graphs

7/22/2019 8-3ws

2/2

horizontal asymptotenone

vertical asymptotex = 0

Name Class Date

8-3Practice (continued) Form G

21. Howmanymillilitersof0.75%sugarsolutionmustbeaddedto100mLof1.5% sugarsolution to form a 1.25% sugar solution?

22. Asoccerplayerhasmade3ofhislast24shotsongoal,or12.5%.Howmanymore

consecutive goals does he need to raise his shots-on-goal average to at least 20%?

23.Error Analysis A student listed the asymptotes of the

function2

2

5 6

( 4 4)

x xy

x x x

+ +=

+ +

as shown at the right.

Explain the students error(s). What are the correct

asymptotes?

Sketch the graph of each rational function.

24.( 6)

xy

x x=

25.2

6

xy

x=

26.2

2

1

4

xy

x

=

27.2

2

2 10 12

9

x xy

x

+ +=

28. Youstartabusinessword-processingpapersforotherstudents.Youspend $3500 on

a computer system and office furniture. You figure additional costs at $.02 per page.

a.Writearationalfunctionmodelingthetotalaveragecostperpage.

Graph the function.

b.Whatisthetotalaveragecostperpageifyoutype1000pages?If you

type 2000?

c.Howmanypagesmustyoutypetobringyourtotalaveragecost to less

than $1.50 per page?

d.Whataretheverticalandhorizontalasymptotesofthegraphofthe

function?

Prentice Hall Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.

24

Rational Functions and Their Graphs