Section 4.2

Properties of Rational Functions

OBJECTIVE 1

2

2

2 2

2

Find the domain of the following rational functions:

4 6(a) (b)

4 8 12

5 9 4(c) (d) (e)

2 3 2

x xR x R x

x x x

x x xR x R x R x

x x

2

1Graph the rational function: 2

3R x

x

OBJECTIVE 2

x

xxR

3

5 2

22

3

xx

xxH

45

12

xx

xxF

2

2

3 2

4

x xG x

x

OBJECTIVE 3

2

Find the horizontal asymptotes, if any, of the graph of

3

2 5

xR x

x x

2

2

Find the horizontal or oblique asymptotes, if any, of the graph of

2 7 1

2

x xH x

x

6 3

6 5 4 3

Find the horizontal or oblique asymptotes, if any, of the graph of

5 4 3

2 5 8 7 2

x xR x

x x x x

2

Find the horizontal or oblique asymptotes, if any, of the graph of

4 1

2

x xG x

x