Why isn't choice C a function? It's because we have the input x = 4 lead to more than one output at the same time (y = 5 and y = -5). A function must have all allowed inputs lead to exactly one output.
The diagram for choice C shows we have the points (4,5) and (4,-5). If we plotted those two points, then a vertical line forms, which will show this relation fails the vertical line test.
Choices A, B, and D do not have this happen where a certain input leads to multiple outputs at once; therefore, these are all functions. For the tables A and D, note there aren't any repeated x values. If you were to convert choice C into table form, then you would have the x value 4 repeat itself.
Out of all the choices only C does NOT represent y as a function of x.
A function is defined as a relation between the set of inputs having exactly one output each.
We have the input x = 4 lead to more than one output at the same time (y = 5 and y = -5). A function must have all allowed inputs lead to exactly one output.
WE can see that the diagram for choice C shows we have the points (4,5) and (4,-5). If we plotted those two points, then a vertical line forms, which will show this relation fails the vertical line test.
Choices A, B, and D do not have this happen where a certain input leads to multiple outputs at once.
Therefore, these are all functions.
For the tables A and D, note there aren't any repeated x values. If we were to convert choice C into table form, then we would have the x value 4 repeat itself.
Hence, Choice C does NOT represent y as a function of x.
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