1. The problem is to sketch the graph of the function $h(x) = \log_2(x + 2)$ and state its domain, range, and asymptote. 2. The logarithmic function $\log_b(x)$ is defined only for $x > 0$. For $h(x) = \log_2(x + 2)$, the argument is $x + 2$, so the domain is where $x + 2 > 0$. 3. Domain: Solve $x + 2 > 0$ which gives $x > -2$. 4. Range: The logarithmic function can take any real value, so the range is $(-\infty, \infty)$. 5. Vertical asymptote: The logarithmic function has a vertical asymptote where the argument is zero, so at $x + 2 = 0$ or $x = -2$. 6. Key point: When $x = -1$, $h(-1) = \log_2(-1 + 2) = \log_2(1) = 0$. 7. The graph is a logarithmic curve shifted left by 2 units, with a vertical asymptote at $x = -2$. Final answers: - Domain: $x > -2$ - Range: $(-\infty, \infty)$ - Vertical asymptote: $x = -2$