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More Graphing
Intercepts and Asymptotes:
Given an equation of the form:
f(x) = P(x) / Q(x) in reduced form;
If (x - a)n (where n is a positive integer) is a
factor of either P(x) or Q(x) and if (x - a)n+1 is a
factor of neither , then
a. The graph crosses the x axis at x = a if and only if n is
odd.
b. The graph stays on the same side of the x axis at x = a if and
only if n is even.
Vertical Asymptotes:
The line x = a is a vertical asymptote of the function f
if at least one of the following statements are true:
| limx®a+
f(x) = +¥ |
limx®a+
f(x) = -¥ |
| limx®a-
f(x) = +¥ |
limx®a-
f(x) = -¥ |
Horizontal Asymptotes:
The line y = b is a horizontal asymptote of the function f
if at least one of the statements is true:
limx®+¥ f(x) = b
or limx®-¥ f(x) = b
Slant Asymptotes:
The line y = ax + b is a slant asymptote of a function f
if:
limx®± ¥ [ f(x) -
(ax + b)] = 0
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