Return to Assignments Fractional functions and graphs
Assignment 2
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
This is still a quite simple fractional function. The vertical asymptote is 
. We find the horizontal asymptote by investigating the line to which the graph approaches if 
and that is 
. The graph intersects the -axis at 
. The graph has no intersection point with the -axis, because the -axis is an asymptote. This result can also be obtained by solving the equation with : this equation has no solution.
The graph is depicted in the following figure.
