# What is an asymptote?

Jan 28, 2015

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 $y = \frac{1}{x}$
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 $0$ $\left(x \to \infty\right)$

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.