 A rational function f is the
quotient of polynomial functions defined by
P(x) and D(x) so that
f (x) = P(x)/D(x)
where D(x) does not equal 0
 Discontinuities of rational functions are either
deleted points or vertical asymptotes.
 Asymptotes
Let f (x) = P(x)/D(x)
where P is a polynomial function with leading
coefficient P and D is a polynomial function with
leading coefficient d. Moreover, P(x) and
D(x) and have no common factors
Vertical
The vertical asymptote is the line x = c
where D(c) = 0. That is, values that cause
division by 0.
Horizontal
If P(x) has degree m and D(x)
has degree n , then the horizontal asymptote is y
= 0 if m < n and it is the horizontal line y
= P /d
if m = n.
Oblique
If the degree of P is one more than the degree of
D, then carry out the division to find the oblique
asymptote y = mx + b.
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© 2011 Karl J. Smith. All rights reserved. 