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