Question: This is the graph of a linear function.
What is the range 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: a green ray with a closed dot at $(3, 5)$ and extending down to the right; position_hint: center
1. **Problem Statement:** We are given a graph of a linear function represented by a green ray starting at the point $(3, 5)$ with a closed dot and extending down to the right.
2. **Understanding the Range:** The range of a function is the set of all possible $y$-values that the function can take.
3. **Analyzing the Graph:** The ray starts at the point $(3, 5)$, which means the function has a value of $y = 5$ at $x = 3$.
4. Since the ray extends downwards to the right, the $y$-values decrease from $5$ to smaller values as $x$ increases.
5. Therefore, the smallest $y$-value is not bounded below (it goes down indefinitely), but the largest $y$-value is $5$.
6. **Range in Inequality Form:** The range includes $y = 5$ (closed dot) and all values less than $5$, so the range is $$y \leq 5$$.
7. **Final Answer:** The range of the function is $$y \leq 5$$.