9.3 Graphing Rational Functions

Algebra II w/ trig

Remember a rational number is a number that can be written as a fraction. Therefore, a rational function is an equation of the form , where p(x)

and q(x) are polynomial expressions and q(x) ≠ 0.

)(

)()(

xq

xpxf

Definitions:- Vertical Asymptotes: a line that the graph

approaches but never intersects- To find the vertical asymptotes: set the denominator equal

to 0 and solve for x (in other words, your excluded values)- Horizontal Asymptotes: a line that the graph

approaches and may intersect- There is at most one horizontal asymptote (y=#)

- 3 conditions, based on the equation

1. If n=m, then

2. If n<m, then y=0

3. If n>m, then there is no horizontal asymptote

...

...

m

n

cx

bxy

c

by

- X-intercepts: the point(s) in which the graph crosses the x axis

- To find the x intercepts, set the numerator equal to 0 and solve.

- Y-intercepts: the point(s) in which the graph crosses the y axis

- To find the y intercepts, set x equal to 0 in the entire polynomial and solve.

- Hole: a point on the graph that does not exist- To find holes factor the numerator and denominator, if any part cancels out, then there is a hole where that part is equal to zero

I. Identify the holes, x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes, then graph by making a table of values. State the domain and range.

A. 12

3

x

xy

B. C. x

y1

12

x

xy

D. E.4

32

2

x

xy

xx

xxy

33

162

3

F. 483

822

23

x

xxxy