Question

six graphs are shown below. click on the tabs to see them.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6
check the box corresponding to each graph that represents a function.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6 none of the gra

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if no vertical line intersects it more than once.

Step1: Analyze Graph 5

For Graph 5, we look at the x - values of the points. The x - value of 3 (let's assume the x - coordinate of the non - single - x - value points is 3) has multiple y - values (since there are multiple points with the same x - coordinate). When we apply the vertical line test, a vertical line at \(x = 3\) will intersect the graph at more than one point. So Graph 5 does not represent a function. Wait, but the question is about which graphs represent functions. Wait, maybe we need to re - evaluate. Wait, the points in Graph 5: let's list the coordinates. Let's assume the grid has integer coordinates. Let's say the points are: (- 5, - 2), (3, - 1), (3, - 3), (3, - 5), (4, 0). For the x - value of 3, we have three different y - values (- 1, - 3, - 5). So a vertical line through \(x = 3\) will intersect the graph at three points. So by the vertical line test, Graph 5 is not a function. But the original checkboxes: Graph 2 and Graph 4 are checked. Wait, maybe we need to consider the other graphs. But since the question is about Graph 5, we can see that it fails the vertical line test.

Answer:

Graph 5 does not represent a function (so the box for Graph 5 should remain unchecked).