Step 1: Understand the definition of a function. A graph represents a function if it passes the vertical line test. This means that any vertical line drawn through the graph intersects the graph at most once. If a vertical line intersects the graph at two or more points, then the graph does not represent a function. Step 2: Apply the vertical line test to Graph 1. Graph 1 shows a diamond shape. Consider the vertical line $x=0$ (the y-axis). This line passes through the points $(0, 1)$ and $(0, -1)$ on the graph. Since the vertical line $x=0$ intersects the graph at two different points, Graph 1 fails the vertical line test. Step 3: Conclude whether Graph 1 is a function. Because Graph 1 fails the vertical line test, it does not represent a function. Therefore, the box for Graph 1 should not be checked. Graph 1 is not a function.