Subjects algebra

Domain Range 636638

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1. **State the problem:** Find the domain and range of the exponential function described. 2. **Recall the general form and properties:** An exponential function typically has the form $$y = a^{x} + k$$ where $a > 0$ and $a \neq 1$, and $k$ is a vertical shift. 3. **Analyze the given information:** The function has a horizontal asymptote at $y = -8$, which means $k = -8$. 4. **Domain:** Exponential functions are defined for all real $x$, so the domain is $$\{x \mid x \in \mathbb{R}\}$$. 5. **Range:** Since the graph approaches $y = -8$ from above and increases toward $0$ as $x$ approaches $0$ from the left, the range is $$\{y \mid y > -8\}$$. 6. **Summary:** - Domain: $$\{x \mid x \in \mathbb{R}\}$$ - Range: $$\{y \mid y > -8\}$$