1. The problem asks to write the domain and range of the graph described in example 16, which is an increasing curve with a vertical asymptote near $x = -5$ and crossing near $(-4, 0)$.
2. The domain of a function is the set of all possible input values ($x$-values) for which the function is defined. A vertical asymptote at $x = -5$ means the function is not defined at $x = -5$. Since the curve crosses near $(-4, 0)$ and is increasing, the domain includes all real numbers except $x = -5$.
3. In set-builder notation, the domain is written as $\{x \mid x \neq -5\}$. In interval notation, this is $(-\infty, -5) \cup (-5, \infty)$.
4. The range is the set of all possible output values ($y$-values). Since the curve is increasing and has a vertical asymptote, the range is all real numbers $(-\infty, \infty)$. In set-builder notation, the range is $\{y \mid y \in \mathbb{R}\}$.
5. Final answers:
- Domain: $\{x \mid x \neq -5\}$ or $(-\infty, -5) \cup (-5, \infty)$
- Range: $\{y \mid y \in \mathbb{R}\}$ or $(-\infty, \infty)$
Domain Range 7D39Bb
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