Return to Assignments Fractional functions and graphs

### Assignment 6

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 function looks slightly different than we are used to, but after a few calculations we come on familiar ground.

We rewrite:

Now this function has the familiar form.

The vertical asymptote of this function is , i.e. the value for which the denominator equals . We find the horizontal asymptote by trying to find the value of if or and that is , thus the -axis. Furthermore we notice that the intersection point with the -axis (take ) is . There is no intersection point with the -axis because the -axis is an asymptote.

The graph is depicted in the following figure.