Question

How do you find the asymptotes for `y=1/(2-x)`?

Answer 1

vertical asymptote at x = 2?
horizontal asymptote at 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 is the equation.

horizontal asymptotes occur as `lim_(x→±∞) f(x) → 0`

If the degree of the numerator is less than the degree 0f the denominator then the equation is y = 0.

here the degree of numerator < degree of denominator and so equation of horizontal asymptote is y = 0
here is the graph of the function as an illustration of them.
graph{1/(2-x) [-10, 10, -5, 5]}