Return to Assignments Fractional functions and graphs
Assignment 4
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 of this function is . We find the horizontal asymptote by taking
or
. We get
because the second term approaches
and then
approaches
. The intersection point with the
-axis is found by substituting
in the formula. We get the intersection point with the
-axis by substituting
and solving the equation:
The solution is