1. The problem is to find the limit $$\lim_{x \to -\infty} e^{-x}$$. 2. Recall the exponential function rule: for any real number $a$, $e^a$ grows very fast as $a$ increases. 3. When $x \to -\infty$, the expression $-x$ becomes very large positive because multiplying a very large negative number by $-1$ makes it very large positive. 4. So, as $x \to -\infty$, $-x \to +\infty$. 5. Therefore, $$e^{-x} = e^{(+\infty)}$$ which tends to infinity. 6. Hence, $$\lim_{x \to -\infty} e^{-x} = +\infty$$. This means the function grows without bound as $x$ approaches negative infinity.