Question

What are the asymptote(s) and hole(s), if any, of `f(x)= 1/(2-x)`?

Answer 1

The asymptotes of this function are x=2 and y=0.

Explanation:

`1/(2-x)` is a rational function. That means that the shape of the function is like this:
graph{1/x [-10, 10, -5, 5]}
Now the function `1/(2-x)` follows the same graph structure, but with a few tweaks. The graph is first shifted horizontally to the right by 2. This is followed by a reflection over the x-axis, resulting in a graph like so:
graph{1/(2-x) [-10, 10, -5, 5]}
With this graph in mind, to find the asymptotes, all that's necessary is looking for the lines the graph won't touch. And those are x=2, and y=0.