1. The problem asks for the domain, range, and asymptote of the function $$h(x) = 2^{x+4}$$. 2. Recall that for an exponential function of the form $$f(x) = a^{x+c}$$ where $$a > 0$$ and $$a \neq 1$$: - The domain is all real numbers, $$\mathbb{R}$$, because you can input any real number into the exponent. - The range is $$y > 0$$ because exponential functions with positive bases never produce zero or negative values. - The horizontal asymptote is $$y = 0$$, since as $$x \to -\infty$$, $$a^{x+c} \to 0$$. 3. Applying these rules to $$h(x) = 2^{x+4}$$: - Domain: $$\{x \mid x \in \mathbb{R}\}$$ (all real numbers) - Range: $$\{y \mid y > 0\}$$ - Asymptote: $$y = 0$$ 4. The shift inside the exponent $$x+4$$ moves the graph left by 4 units but does not affect domain, range, or asymptote. 5. Therefore, the correct choice is: $$\text{domain: } \{x \mid x \in \mathbb{R}\}; \quad \text{range: } \{y \mid y > 0\}; \quad \text{asymptote: } y = 0$$