Question

How to find the asymptotes of `f(x) = 3 / (3 - x)` ?

Answer 1

vertical asymptote x = 3

horizontal asymptote y=0

Explanation:

Vertical asymptotes can be found when the denominator

of a rational function is zero.

hence 3 - x = 0 → x = 3 is a vertical asymptote.

[ If the degree of the numerator is less than the degree of

the denominator of a rational function then y = 0 is a
horizontal asymptote ]

here degree of numerator is 0 and degree of denominator 1

hence horizontal asymptote at y = 0

Here is the graph of the function to illustrate them.

graph{3/(3-x) [-10, 10, -5, 5]}