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Coolmath Precalculus Review Calculus Preview
Lesson 19 - Graphing - Rational Functions: The Whole Thing
(page 5 of 10)
---- This Precalculus review (Calculus preview) lesson explains how to put all the pieces (intercepts and asymptotes) together to graph rational functions.

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Let's do another one:

Graph

2 things
and
2 sentences!

The y-intercept: Find f(0)

f( 0 ) = ( 3( 0 ) ) / ( ( 0 )^2 + 2( 0 ) - 8 ) = 0

( 0 , 0 ) nowhere else

The x-intercept: numerator = 0, solve.

( 0 , 0 ) nowhere else

Vertical asymptotes: denominator = 0, solve

x^2 + 2x - 8 = 0 ... ( x - 2 )( x + 4 ) = 0 ... x = 2 , x = -4

Horizontal asymptote:

Look at

The line y = 0 ( the x-axis )

* When this is the case, we're going to be forced to "quickie plot" a few points to nail the graph. No, this isn't being a sissy -- we'll have no choice. But, Calculus will fix this problem by telling us where the graphs are increasing and decreasing!

Continued on the next page

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