1. **Problem Statement:** We are given the function $y = \ln(4 - x)$ and need to find its domain and the equation of its asymptote. 2. **Recall the domain rule for logarithmic functions:** The argument inside the logarithm must be positive. That is, for $y = \ln(u)$, the domain requires $u > 0$. 3. **Apply the domain rule:** Here, the argument is $4 - x$. So, $$4 - x > 0$$ 4. **Solve the inequality:** $$4 > x$$ $$x < 4$$ 5. **Domain:** The domain of $y = \ln(4 - x)$ is all real numbers less than 4, or in interval notation: $$(-\infty, 4)$$ 6. **Asymptote:** The logarithmic function has a vertical asymptote where its argument approaches zero from the right. That is, $$4 - x = 0 \implies x = 4$$ So, the vertical asymptote is the vertical line: $$x = 4$$ **Final answers:** - Domain: $(-\infty, 4)$ - Vertical asymptote: $x = 4$