1. **State the problem:** We are given a graph of a V-shaped figure and asked to determine the domain, range, whether it is a function or relation, and explain why. 2. **Analyze the graph:** - The graph is V-shaped, descending from point (-5,5) to (0,0), then ascending from (0,0) to (5,0). - The left arm goes from $x=-5$ to $x=0$ with $y$ decreasing from 5 to 0. - The right arm goes from $x=0$ to $x=5$ with $y$ constant at 0. 3. **Domain:** The domain is all $x$ values covered by the graph. - From the graph, $x$ ranges from $-5$ to $5$. - So, domain is $$[-5,5]$$. 4. **Range:** The range is all $y$ values covered by the graph. - The highest $y$ is 5 at $x=-5$. - The lowest $y$ is 0 at $x=0$ and $x=5$. - So, range is $$[0,5]$$. 5. **Function or relation:** - A function assigns exactly one $y$ value for each $x$ value. - Check if any vertical line crosses the graph more than once. - For each $x$ in $[-5,5]$, there is exactly one $y$ value. - Therefore, it is a **function**. 6. **Explanation:** - The graph passes the vertical line test. - Each input $x$ has a unique output $y$. 7. **Summary:** - Domain: $$[-5,5]$$ - Range: $$[0,5]$$ - It is a function because each $x$ corresponds to exactly one $y$.