1. **Problem statement:** Find the limit of the function $f(x) = e^{-x}$ as $x$ approaches positive infinity. 2. **Recall the function and limit concept:** The function is $f(x) = e^{-x} = \frac{1}{e^x}$. We want to find $$\lim_{x \to +\infty} e^{-x}.$$ This means we want to see what value $e^{-x}$ approaches when $x$ becomes very large. 3. **Evaluate the limit:** As $x$ increases, $e^x$ grows very large (tends to infinity). Therefore, $$e^{-x} = \frac{1}{e^x}$$ becomes $$\frac{1}{\text{very large number}}$$ which tends to 0. 4. **Conclusion:** The limit is $$\lim_{x \to +\infty} e^{-x} = 0.$$ This means the graph approaches the x-axis but never touches it, which is called an asymptote. This matches the description of the curve approaching zero as $x$ increases.