Precalculus Examples

$\frac{x}{\sqrt{x}}$

Step 1

Find where the expression $\frac{x}{\sqrt{x}}$ is undefined.

$x \leq 0$

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Since the limit does not exist, there are no horizontal asymptotes.

No Horizontal Asymptotes

Step 4

Use polynomial division to find the oblique asymptotes. Because this expression contains a radical, polynomial division cannot be performed.

Cannot Find Oblique Asymptotes

Step 5

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

Cannot Find Oblique Asymptotes

Step 6