Question

which graph represents a function?

Explanation:

To determine which graph represents a function, we use the vertical line test. A graph represents a function if no vertical line intersects the graph at more than one point.

Step 1: Analyze the first graph

In the first graph, we check for vertical lines. For example, at \( x = -4 \) and \( x = -3 \), there are points, but no vertical line intersects more than one point. Wait, actually, looking at the second graph: at \( x = 4 \), there are two points (y = 3 and y = 4), so it fails the vertical line test. The third graph (assuming the last one) has points where each x - value has only one y - value. Wait, let's re - examine:

First graph: Let's list the points. The points seem to be at (-4,1), (-3,1), (-1,2), (4,3). For any vertical line (x = a), we have at most one point.

Second graph: Points at (-3,1), (4,3), (4,4). Here, when \( x = 4 \), we have two points (y = 3 and y = 4), so it fails the vertical line test.

Third graph: Let's assume the points are such that each x has a unique y. So the third graph (the bottom one) passes the vertical line test. Wait, maybe I misread the first two. Wait, the first graph (top) has points at x=-4 (y=1), x=-3 (y=1), x=-1 (y=2), x=4 (y=3). Wait, x=-4 and x=-3 are different x - values, so that's okay. The second graph (middle) has x = 4 with two y - values (3 and 4), so it fails. The third graph: let's say the points are at different x - values, so each x has one y. So the third graph (the bottom one) represents a function.

Answer:

The third graph (the bottom - most graph) represents a function. (If we consider the options as circles next to them, the circle next to the third graph should be selected. Since the user's image has three graphs with circles, the correct one is the third graph's circle.)