You can
put this solution on YOUR website! What does a rational function look like (example: f(x)=x+5 / (over) X+1
They always have at least one asymptote, which is a straight line they get as
close to as we please yet never touch. Tha graph of
x+5
f(x) = -----
x+1
looks like this. The asymptotes are drawn in. The red line and the green line
are not themselves part of the graph of f(x). Only the red curves is the graph
of f(x). Notice that the red curves get closer and closer to the red vertical
line thru -1 on the x-axis both above and below. So that red vertical line is
its vertical asymptote. Notice that the red curve also gets closer and closer
on the right and left to the green horizontal line through 1 on the y-axis.
Rational functions can also have slanted asymptotes such as the graph of
x³+x²-1
f(x) = ---------
x²+3
Notice that the red curve approaches the green slanted line above to the
right as well as below to the left. Notice also that the red line crosses
its asymptote approximately at the point (-1.3, -.3). A curve may cross its
asymptote but eventually it will only approach it and never reach it
again (if it crossed it before).
Edwin
