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More Graphing

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

 

Subject: 
Calculus
Subject X2: 
Calculus

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