Question

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

Answer 1

vertical asymptote at x = 2
horizontal asymptote at y= 0 (x-axis)

Explanation:

Vertical asymptote occur when the denominator of a rational

function is zero. They can be found by equating the
denominator to zero.

hence x - 2 = 0 gives x = 2.

[ If the degree of the numerator < degree of denominator then

there will be a horizontal asymptote at y = 0 ]

Here is the graph of f(x) to illustrate:
graph{1/(x-2) [-10, 10, -5, 5]}