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 th

Explanation:

Step1: Recall the vertical line test

A graph represents a function if and only if no vertical line intersects the graph more than once.

Step2: Analyze Graph 1

For Graph 1 (the circle), we can draw a vertical line (e.g., \(x = 0\)) that intersects the circle at two points (e.g., \((0, 1)\) and \((0, - 1)\) approximately). So, by the vertical line test, Graph 1 does not represent a function. Since we only have Graph 1 shown here (and we need to check each, but for Graph 1 specifically), it fails the vertical line test. If all other graphs (Graph 2 - Graph 6) are not shown, but based on Graph 1, we can say about Graph 1 first. But the question is to check boxes for each graph that is a function. Since Graph 1 is a circle, it's not a function. If we assume we need to answer about Graph 1 first (and the rest are not shown, but the user provided Graph 1), then Graph 1 is not a function. But the options include "None of the above" if none are functions. But we need to check each. However, since only Graph 1 is visible, and it's not a function, we need to see. Wait, the problem is to check the box for each graph that represents a function. For Graph 1, since it's a circle, vertical line test fails, so it's not a function. So the box for Graph 1 should not be checked. If all other graphs (2 - 6) are also not functions (but we don't see them), then "None of the above" would be checked. But since we only have Graph 1 shown, and it's not a function, we can say that Graph 1 is not a function. But the question is to check boxes for each that is a function. So for Graph 1, the answer is that it's not a function, so its box is not checked.

Answer:

For Graph 1: The box corresponding to Graph 1 is not checked (as it fails the vertical line test). If all other graphs (2 - 6) also fail the vertical line test (assuming, since we don't see them, but if we have to answer based on Graph 1 and the "None of the above" option), then the box for "None of the" (assuming "None of the above" is the full option) would be checked. But based on Graph 1 alone, since it's not a function, and we don't have info on others, but the problem is to check each graph that is a function. So for Graph 1, the answer is that it's not a function, so we don't check its box. If we have to choose from the given options for Graph 1: \(\boldsymbol{\text{Graph 1}}\) is not a function, so its box is unchecked. If all graphs (1 - 6) are not functions, then "None of the" (the option) would be checked. But since only Graph 1 is shown and it's not a function, we can say that Graph 1 is not a function, so we don't check its box.