Finite Math Examples

$\sqrt{\frac{25}{y}}$

Step 1

Find where the expression $\sqrt{\frac{25}{y}}$ is undefined.

$y \leq 0$

Step 2

Since $\sqrt{\frac{25}{y}}$ $\to$ $\infty$ as $y$ $\to$ $0$ from the left and $\sqrt{\frac{25}{y}}$ $\to$ $\infty$ as $y$ $\to$ $0$ from the right, then $y = 0$ is a vertical asymptote.

$y = 0$

Step 3

$x = \sqrt{\frac{25}{y}}$ is an equation of a line, which means 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.

Vertical Asymptotes: $y = 0$

No Horizontal Asymptotes

Cannot Find Oblique Asymptotes

Step 6