Properties of Rational Functions

Vertical Asymptotes come from…

the denominator AFTER canceled common factors.

Zeros come from…

the numerator AFTER you’ve canceled common factors.

Holes come from…

x = the canceled factor (set = to zero)

y = plugging the factor = to zero into the simplified function.

The domain of a rational function is…

all real numbers EXCEPT those that make the denominator = 0

n equals…

the degree of the numerator

m equals…

the degree of the denominator

n < m

horizontal asymptote is y = 0

n = m

horizontal asymptote is y = a/b, where a is the LC of the numerator, and b is the LC of the denominator

n > m

there is no horizontal asymptote (check for oblique)

if the degree of the numerator is exactly 1 more than that of the denominator…

there is an oblique/slant asymptote.

To find the oblique asymptote…

use long division