Understand the behavior of the exponential function e^x.

The exponential function $e^x$ is a continuous function that is always positive. As the value of $x$ decreases, the value of $e^x$ also decreases.

As $x$ becomes a very large negative number (approaches $-\infty$), the value of $e^x$ approaches 0.
For example:
$e^{-1} \approx 0.368$
$e^{-10} \approx 0.000045$
$e^{-100}$ is an even smaller positive number.
Therefore, as $x \to -\infty$, $e^x \to 0$.