# How do you find vertical, horizontal and oblique asymptotes for y=1/(2-x)?

Apr 10, 2016

vertical asymptote x = 2
horizontal asymptote y = 0

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve: 2 - x = 0 → x = 2

$\Rightarrow x = 2 \text{ is the asymptote }$

Horizontal asymptotes occur as ${\lim}_{x \to \pm \infty} f \left(x\right) \to 0$

When the degree of the numerator < degree of the denominator, as is the case here then the equation is always
y=0

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here hence there are no oblique asymptotes.

Here is the graph of the function.
graph{1/(2-x) [-10, 10, -5, 5]}