1. **State the problem:** We need to determine the end behavior of the function $f(x) = \ln(x - 3)$. 2. **Recall the domain and properties of logarithmic functions:** The natural logarithm function $\ln(x)$ is defined only for $x > 0$. For $f(x) = \ln(x - 3)$, the inside of the logarithm must be positive, so $x - 3 > 0 \Rightarrow x > 3$. This means the domain of $f$ is $(3, \infty)$. 3. **Vertical asymptote:** Since the function is undefined at $x = 3$, there is a vertical asymptote there. As $x$ approaches 3 from the right, $x - 3$ approaches 0 from the positive side, and $\ln(x - 3)$ approaches $-\infty$. 4. **End behavior as $x \to \infty$:** As $x$ becomes very large, $x - 3$ also becomes very large, so $\ln(x - 3) \to \infty$. 5. **Summary:** - As $x \to 3^+$, $f(x) \to -\infty$. - As $x \to \infty$, $f(x) \to \infty$. 6. **Match with given options:** This matches option A. **Final answer:** A as $x \to 3$, $f(x) \to -\infty$, and as $x \to \infty$, $f(x) \to \infty$.