Question

What is an asymptote?

Answer 1

An asymptote is a value of a function that you can get very near to, but you can never reach.

Let's take the function `y=1/x`
graph{1/x [-10, 10, -5, 5]}
You will see, that the larger we make `x` the closer `y` will be to `0`
but it will never be `0` `(x->oo)`

In this case we call the line `y=0` (the x-axis) an asymptote

On the other hand, `x` cannot be `0` (you can't divide by`0`)

So the line `x=0` (the y-axis) is another asymptote.