# How do you find the vertical, horizontal and slant asymptotes of: Y=(3x)/(x^2-x-6) + 3?

Nov 25, 2016

Horizontal asymptote y=3
Vertical asymptotess x=3 and x=-2
No slant asymptotes.

#### Explanation:

In case of rational functions, like the one given here, horizontal asymptotes are horizontal lines which the function approaches as $x \to \infty$. In the present case, as $x \to \infty$ y=3. Hence y=3 is an horizontal asymptote of the given function.

For vertical asymptotes, in case of rational functions, it has to be seen that for what values of x, $y \to \infty$. In the present case if the denominator is factorised the function can be written as $y = \frac{x}{\left(x - 3\right) \left(x + 2\right)} + 3$. For x=3 and x=-2, $y \to \infty$. Hence vertical asymptotes are x=3 and x=-2.

There are no slant asymptotes.