Return to Assignments Fractional functions and graphs
Assignment 3
Given the function:
Find:
the vertical asymptote;
the horizontal asymptote;
the intersection point with the -as if it exists;
the intersection point with the -as if it exists.
Based on these results sketch the result in the figure.
Solution
The vertical asymptote is . We find the horizontal asymptote when
or
and that is
, because the second term approaches
and thus
approaches
. The intersection point with the
-axis is
. This result can be obtained by substituting
in the function. The intersection point with the
-as is obtained by substituting
and solving the following equation:
The solution is:
See the graph in the following figure: