1. **State the problem:** We are given the function $f(x) = \frac{3}{5} 4^x$ and need to write the limit statements for its left and right end behaviors. 2. **Recall the behavior of exponential functions:** For $a^x$ where $a > 1$, as $x \to \infty$, $a^x \to \infty$ (exponential growth), and as $x \to -\infty$, $a^x \to 0$. 3. **Apply this to $f(x)$:** Since $4 > 1$, $4^x$ grows exponentially. 4. **Left end behavior:** As $x \to -\infty$, $4^x \to 0$, so $$\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} \frac{3}{5} 4^x = \frac{3}{5} \times 0 = 0.$$ 5. **Right end behavior:** As $x \to \infty$, $4^x \to \infty$, so $$\lim_{x \to \infty} f(x) = \lim_{x \to \infty} \frac{3}{5} 4^x = \infty.$$ 6. **Classify the function:** Since the base $4 > 1$, $f(x)$ is an exponential growth function. Final answers: - Left: $\lim_{x \to -\infty} f(x) = 0$ - Right: $\lim_{x \to \infty} f(x) = \infty$ - Classification: Exponential growth