Question

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 graphs

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (y - value). We use the vertical line test: if any vertical line intersects the graph at more than one point, it is not a function.

Step2: Analyze Graph 2

For Graph 2, look at the x - value of 0 (the y - axis). There are two points with \(x = 0\) (one at \(y = 0\) and one at \(y = 2\)). So a vertical line at \(x = 0\) would intersect the graph at two points. Thus, Graph 2 does not pass the vertical line test and is not a function. Wait, but the question is about which graphs represent functions. Wait, maybe I misread. Wait, the given Graph 2 (the one shown) has multiple points for x = 0? Wait, no, let's re - check. Wait, the points in Graph 2: let's list the coordinates. From the graph, the points seem to be: (-5, -1) (or whatever the left - most point is), (-2, -4), (-1, -2), (0, 0), (0, 2), (4, -2). Wait, at x = 0, there are two points (0, 0) and (0, 2). So vertical line x = 0 intersects twice. So Graph 2 is not a function. But the first graph (Graph 1) - wait, the user's image shows Graph 1 is checked? Wait, maybe I made a mistake. Wait, no, the problem is to check the box for each graph that represents a function. Let's re - apply the vertical line test.

For a graph to be a function, every x has at most one y. So for Graph 2, since there are two points with the same x - value (x = 0), it is not a function. So Graph 2 should not be checked. But the initial check in the image is for Graph 1. Wait, maybe the user's question is about Graph 2? Wait, no, the question is "Check the box corresponding to each graph that represents a function." Let's re - evaluate Graph 2.

Looking at the points in Graph 2: the x - coordinates. Let's list the x - values of the points. Let's assume the points are: (-5, -1), (-2, -4), (-1, -2), (0, 0), (0, 2), (4, -2). So x = 0 has two y - values (0 and 2). So by vertical line test, Graph 2 is not a function. So the box for Graph 2 should not be checked.

Wait, but maybe I misread the graph. Wait, the graph in the image: the points are plotted. Let's see the x - axis. The origin is (0,0), and there is a point at (0,0) and (0,2). So same x, different y. So Graph 2 is not a function. So the answer for Graph 2 is that it does not represent a function, so the box for Graph 2 should not be checked. But the question is to check the box for each graph that represents a function. So if Graph 2 does not represent a function, we do not check its box.

Answer:

The box for Graph 2 should not be checked (i.e., the checkbox next to "Graph 2" remains unchecked because Graph 2 fails the vertical line test and does not represent a function).