Algebra Examples

$\frac{x}{y} = y - 6$

Step 1

Find where the expression $y - 6$ is undefined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

$\frac{x}{y} = y - 6$ is an equation of a line, which means there are no horizontal asymptotes.

No Horizontal Asymptotes

Step 4

The oblique asymptote is a slant asymptote along the linear line of the graph, which is the linear portion of the long division result that was calculated when the expression was reduced.

$y = y - 6$

Step 5

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

Oblique Asymptotes: $y = y - 6$

Step 6