Question

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

Answer 1

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

`rArr x = 2" is the asymptote "`

Horizontal asymptotes occur as `lim_(xto+-oo) f(x) 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]}