http://www.ck12.org Chapter 1. Functions and Graphs
1.9 Asymptotes and End Behavior
Here you will get a conceptual and graphical understanding of what is meant by asymptotes and end behavior. This
will lay the groundwork for future concepts.
Most functions continue beyond the viewing window in our calculator or computer. People often draw an arrow next
to a dotted line to indicate the pattern specifically. How can you recognize these asymptotes?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/57949http://www.youtube.com/watch?v=y78Dpr9LLN0 James Sousa: Summary of End Behavior or Long Run Behavior
of Polynomial Functions
Guidance
A vertical asymptote is a vertical line such asx=1 that indicates where a function is not defined and yet gets
infinitely close to.
A horizontal asymptote is a horizontal line such asy=4 that indicates where a function flattens out asxgets very
large or very small.A function may touch or pass through a horizontal asymptote.
The reciprocal function has two asymptotes, one vertical and one horizontal. Most computers and calculators do not
draw the asymptotes and so they must be inserted by hand as dotted lines.
The reason why asymptotes are important is because when your perspective is zoomed way out, the asymptotes
essentially become the graph.