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: