Question: This is the graph of a linear function.
What is the domain of the function?
Write your answer as an equation like $x = 5$, as an inequality like $y > 3$, or as a compound inequality like $2 \leq x < 4$.
Graph shape: a line segment rising from left to right with open endpoints, from approximately $(-4, -9)$ to $(1, -4)$; position_hint: center.
1. **State the problem:** We are given a graph of a linear function represented by a line segment with open endpoints at approximately $(-4, -9)$ and $(1, -4)$.
2. **Identify the domain:** The domain of a function is the set of all possible $x$-values for which the function is defined.
3. **Analyze the graph:** Since the graph is a line segment starting just after $x = -4$ and ending just before $x = 1$, and both endpoints are open (not included), the domain includes all $x$ values strictly between $-4$ and $1$.
4. **Write the domain as an inequality:** Because the endpoints are open, the domain is expressed as a compound inequality:
$$-4 < x < 1$$
5. **Conclusion:** The domain of the function is all $x$ such that $x$ is greater than $-4$ and less than $1$.