2.10. Horizontal Asymptotes http://www.ck12.org
2.10 Horizontal Asymptotes
Here you will learn to identify when horizontal asymptotes exist, specify their height and write their equation.
Vertical asymptotes describe the behavior of a function as the values ofxapproach a specific number. Horizontal
asymptotes describe the behavior of a function as the values ofxbecome infinitely large and infinitely small. Since
functions cannot touch vertical asymptotes, are they not allowed to touch horizontal asymptotes either?
Watch This
Watch the following video, focusing on the parts about horizontal asymptotes.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/60833http://www.youtube.com/watch?v=wBZxVxiJS9I James Sousa: Determining Horizontal and Vertical Asymptotes
of Rational Functions
Guidance
Horizontal asymptotesare a means of describing end behavior of a function. End behavior essentially is a
description of what happens on either side of the graph as the function continues to the right and left infinitely. When
you are determining the horizontal asymptotes, it is important to consider both the right and the left hand sides,
because the horizontal asymptotes will not necessarily be the same in both places. Consider the reciprocal function
and note how asxgoes to the right and left it flattens to the liney=0.