Subjects algebra

Graph Domain

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1. **Problem Statement:** Determine the domain of the graph described, which starts at $x=-12$ with a closed point and ends at $x=2$ with an open circle. 2. **Understanding Domain:** The domain of a function is the set of all possible input values ($x$-values) for which the function is defined. 3. **Interpreting the Graph Description:** - The graph starts at $x=-12$ with a closed (solid) point, meaning $x=-12$ is included in the domain. - The graph ends at $x=2$ with an open circle, meaning $x=2$ is not included in the domain. - The curve is continuous between these points. 4. **Domain Conclusion:** Since the graph includes all $x$-values from $-12$ up to but not including $2$, the domain is the interval: $$[-12, 2)$$ This means all real numbers $x$ such that $-12 \leq x < 2$. 5. **Summary:** The domain includes the starting point $-12$ (closed point) and excludes the endpoint $2$ (open circle).