Section 9-1

Graphing Rational Functions

Def: A rational function is of the form

Where p(x) and q(x) are rational polynomials and

)(

)()(

xq

xpxf

0)( xq

The line that the graph of a rational function

approaches is called the

_________?________

The line that the graph of a rational function

approaches is called the

_________?________

1.) Graph: 4

2)(

xxf

Note: x cannot equal ___?____because it would be undefined

Note: x cannot equal ___?____because it would be undefined

There are three types of asymptotes1.Vertical2.Horizontal 3.Oblique or Slant

To find horizontal asymptotes:1.If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). 2.If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote. 3.If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

One way to remember this is the following the pnemonic device: BOBO BOTN EATS DC

BOBO BOTN EATS DC

BOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none

EATS DC - Exponents are the same, divide coefficientsl

BOBO BOTN EATS DC

BOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none

EATS DC - Exponents are the same, divide coefficientsl

2.) Graph:

Find the domain and range

x

xxf

1)(

3.) Graph: 3)(2(

6

xxy

4.) Graph: 43

543)(

2

2

xx

xxxf

5.) Graph:

Find the discontinuity

5

25)(

2

x

xxf

Homework

Practice 9-1 and

Page 553

Problems: 1,5,14,15 and 25

Plot your graphs on graph paper

Make sure to label your grid