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.