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

Jun 6, 2016

Use the fact that $\frac{x - 3}{x - 2} = \frac{x - 2 - 1}{x - 2} = \frac{x - 2}{x - 2} - \frac{1}{x - 2} = 1 - \frac{1}{x - 2}$.

#### Explanation:

I suppose you meant oblique asymptote, which intuitively refers to the 'slant' asymptote.

To find asymptotes, we check the $x$ and $y$ values where the function is undefined.

When $x - 2 = 0$, the function is undefined. Thus the vertical asymptote is $x = 2$.

Also, notice that as $x$ gets larger, $\frac{1}{x - 2}$ gets smaller, but never zero. Thus, the function will never take on the value $y = 1$, and thus that is the vertical asymptote.