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's not a function.

Step2: Analyze Graph 5

For Graph 5, check x - values. Let's list the points (approximate coordinates): (-4, 4), (-1, 3), (-1, -2), (3, 5), (3, 1), (2, -5). The x - value - 1 has two y - values (3 and -2), and x - value 3 has two y - values (5 and 1). So a vertical line at x=-1 or x = 3 would intersect twice. Thus, Graph 5 is not a function? Wait, no, wait the original checkboxes: Wait, the question is to check graphs that represent functions. Wait, maybe I misread. Wait, let's re - evaluate. Wait, the points: Let's get precise. Let's assume the coordinates:

First point: x=-4, y = 4 (unique x)

Second: x=-1, y = 3

Third: x=-1, y=-2 (same x, different y)

Fourth: x = 3, y = 5

Fifth: x = 3, y = 1 (same x, different y)

Sixth: x = 2, y=-5

So for x=-1, there are two y - values, so it fails the vertical line test. So Graph 5 does not represent a function? Wait, but maybe I made a mistake. Wait, the initial checkboxes: Graph 1 and Graph 4 are checked. But the question is about Graph 5. So according to the vertical line test, since there are two points with the same x - coordinate (-1 and 3), Graph 5 is not a function. But wait, maybe the user is asking if Graph 5 is a function. So the answer is no, but the question is to check the box if it's a function. So Graph 5 does not represent a function, so the box should not be checked. But maybe I misread the points. Wait, let's look again. The graph has points: Let's see the grid. The x - axis: from -5 to 5, y - axis from -5 to 5.

Point 1: (-4, 4) (x=-4, y = 4)

Point 2: (-1, 3) (x=-1, y = 3)

Point 3: (-1, -2) (x=-1, y=-2) → same x, different y

Point 4: (3, 5) (x = 3, y = 5)

Point 5: (3, 1) (x = 3, y = 1) → same x, different y

Point 6: (2, -5) (x = 2, y=-5)

So yes, x=-1 and x = 3 have multiple y - values. So Graph 5 is not a function. But the question is to check the box if it's a function. So the answer is that Graph 5 does not represent a function, so the box should not be checked. But maybe the user is asking for the correct check. Wait, the original checkboxes: Graph 1 and Graph 4 are checked. But the question is about Graph 5. So the conclusion is Graph 5 is not a function, so the box is not checked. But maybe I made a mistake. Wait, perhaps the coordinates are different. Wait, maybe the second point is x = -2, y = 3? Wait, the grid lines: Let's assume the x - coordinates: the first point is at x=-4 (since 4 units left of origin), then x=-2? Wait, maybe I misread the x - coordinate of the second point. Let's re - examine the graph. The second point: between x=-2 and x = 0? Wait, maybe the x - coordinate is -1? No, maybe the graph is different. Wait, perhaps the points are:

(-4, 4), (-2, 3), (-1, -2), (3, 5), (3, 1), (2, -5). No, that still has x=-1 and x = 3. Wait, maybe the x - coordinates are unique. Wait, maybe I misidentified the x - values. Let's list the x - coordinates of each point:

1. x=-4 (unique)

2. x=-1 (wait, no, maybe x=-2? Let's see the grid. Each square is 1 unit. So from the origin (0,0), moving left 1 is -1, left 2 is -2, left 3 is -3, left 4 is -4. The first point is at x=-4 (left 4), y = 4 (up 4). The second point: left 1? No, left 2? Wait, the second point is at x=-1? No, maybe x=-2. Wait, the third point: x=-1? No, maybe x = -0.5? No, the grid is integer coordinates? Maybe the points are:

(-4, 4), (-1, 3), (-1, -2) → no, same x. So regardless, if two points have the same x, it's not a function. So Graph 5 does not represent a function, so the box should not be checked. But the question is to check the box if it's a function. So the answer is that Graph 5 is not a function, so the box is unchecked. But maybe the user is asking if Graph 5 is a function. So the answer is no, so the box is not checked.

Answer:

The box corresponding to Graph 5 should not be checked (i.e., Graph 5 does not represent a function).