1 The line x a is a vertical asymptote of a function f if fx increases or decreases without bound as

1
1) The line x a is a vertical asymptote of a
function f if f(x) increases or decreases
without bound as x?a.
Note The zeros of the denominator of a rational
function often give vertical asymptotes.
2) The line y b is a horizontal asymptote of a
function f if f(x)?b as x increases or
decreases without bound.
2
Horizontal Asymptote of a Rational Function Let f
be the rational function given by
1)   If n lt m the x-axis is a horizontal
asymptote. 2)   If n m,the line is a
horizontal asymptote. 3) If n gt m, there
is no horizontal asymptote.
3
Slant asymptotes If f(x) p(x)/q(x) and the
degree of p is one greater than the degree of q,
the graph of f has a slant asymptote.
Find the slant asymptote by dividing q(x) into
p(x). Drop the remainder to determine the
equation for the slant asymptote.