1.9. Asymptotes and End Behavior http://www.ck12.org
Example A
Many students have the misconception that an asymptote is a line that a function gets infinitely close tobut does not
touch. This is not true. Identify the horizontal asymptote for the following function.
Solution:
The graph appears to flatten asxgrows larger. The horizontal asymptote isy=0 even though the function clearly
passes through this line an infinite number of times.
Example B
Identify the asymptotes and end behavior of the following function.
Solution:
The function has a horizontal asymptotey=2 asxapproaches negative infinity. There is a vertical asymptote at
x=0. The right hand side seems to decrease forever and has no asymptote.Note that slant asymptotes do exist and
are called oblique asymptotes.
Example C
Identify the asymptotes and end behavior of the following function.