A3 3.5a rational functions and domain

homework: p. 406 1-35 odd

rational expressions:

The DOMAIN of a rational function is determined by the denominator. Whatever values make the denominator = zero (usually done via factoring)

( )( )

( )

p xf x

q x

2 7 9example: find the domain: ( )

( 2)( 5)

x xf x

x x x

2 9

example: find the domain: ( )( 3)

xf x

x

2example: find the domain: ( )

9

xf x

x

2

3example: find the domain: ( )

9

xf x

x

now for a new concept:With every VA (from the denominator) we talk about what happens on the extreme ends of the graph (the end behavior now using big kid notation!) and what happens as we approach each vertical asymptote from the left and from the right.

End Behavior: new notation = limit notation

Approaching vertical asymptotes from the left and the right…

Example: use limit notation for EB and asymptotes:

1 ( )f x

x

examples..Find the vertical asymptotes, sketch graph, discuss the end behavior (limit notation) and the behavior of the graph as you approach each asymptote from the left and the right.

2a. ( )

1

xf x

x

2

2 b. ( )

9

xf x

x

2 4

c. ( )2

xf x

x

whiteboard problemsFind the domain of each rational function.

Find the VA, sketch the graph, then use limit notation to discuss the end behavior, and the behavior at each asymptote as you approach from the left and the right.

22 a. g( )

( 2)( 6)

xx

x x

2

3 b. h( )

4 16

xx

x

2

2 a. f ( )

4 21

xx

x x

2 b. f ( )

3 10

xx

x x