A2 – Section 8.2
Graphing Rational Functions
Rational functions have the form f ( x) 
Date____________
p ( x)
, where p(x) and q(x) are polynomials that
q ( x)
have no common factors other than 1.
Hyperbola: a family of functions whose graph is based on ________________.
x
-3
f ( x) 
1
x
-2
-1
-½
-¼
0
¼
½
1
2
3
Asymptote: a line that the graph ____________________ but usually doesn’t cross
Hyperbolas have:

A __________________ asymptote, __________

A __________________ asymptote, __________

A _____________ that’s limited by the _________________________
Domain = { _____________________________________ }



A _____________ that’s limited by the _________________________
Range = { _____________________________________ }
Two symmetrical parts called branches.
a
 k , where ______________________
A transformation based on f ( x) 
xh
Graphing Hyperbolas using Transformations:
Find the ________________________, based on __________________.
1.
2.
Choose some values for x and create a _________________.
Ex 1
Graph y 
3
2
x 1
Transformation:________
Asymptotes:_____________
Domain:______________
Range:_______________
Graphing Rational Functions (same degree for numerator & denominator):
Find the __________ asymptote(s) by setting the denominator equal to zero
and solving.
Find the __________ asymptote by find the ratio of ____________________.
1.
2.
Choose some x-values between the vertical asymptotes and create a _______.
3.
Ex 2 Graph the general rational function.
f ( x) 
Vertical Asymptote(s):___________________
2x 2  5
x2  x  6
Horizontal Asymptote:___________________
x
f(x)
Domain:__________________ Range:___________________
Horizontal Asymptote Summary
m<n
m=n
m>n