Why does $e^{-x}$ approach $0$ as $x$ gets large?

Question

Why is it that

$$\lim_{x \to -\infty} e^x = 0?$$

Context: College has started back up again and I like to understand the reasons why things do the things they do, rather than just memorizing. I'm sure i've seen it before - but I am coming up with a blank today.

Answer 1

Hint. One may recall that

$$ e^{-x}=\frac1{e^x} $$

Answer 2

The guiding question goes like this: What happens when you divide $1$ by a really, really large number?

Answer 3

Have a look at the graph:

Notice what happens when you go from a negative number to a positive number.