determine whether each graph represents a function. function not a function

Explanation:

Step1: Recall the vertical line test

A graph represents a function if every vertical line intersects the graph at most once. For a set of points, we check if any ( x )-value is repeated (since a vertical line at that ( x )-value would intersect multiple points).

Step2: Analyze the given points

Looking at the points in the graph, let's identify their ( x )-coordinates. Suppose the points have ( x )-coordinates: let's assume the first point (top) has ( x = 2 ) (for example, from the grid), the middle - left point has ( x = 2 ), the middle - right point has ( x = 3 ), and the bottom - right point has ( x = 3 )? Wait, no, actually, looking at the grid, let's list the coordinates. Let's say the points are: (2, 4), (2, 2), (3, 3), (3, 1) (assuming grid lines). Wait, no, maybe better to see: if we have two points with the same ( x )-value (e.g., two points with ( x = 2 ) or two with ( x = 3 )), then the vertical line at ( x = 2 ) (or ( x = 3 )) would intersect two points. Wait, actually, in the given graph, let's check the ( x )-coordinates of the points. Let's assume the points are: one with ( x = 2 ) (top), one with ( x = 2 ) (middle - left), one with ( x = 3 ) (middle - right), one with ( x = 3 ) (bottom - right). So for ( x = 2 ), there are two ( y )-values (so two points), and for ( x = 3 ), there are two ( y )-values. So by the vertical line test, since there are ( x )-values (like ( x = 2 ) and ( x = 3 )) that have more than one ( y )-value, the graph does not represent a function.

Answer:

Not a Function