Answer:
No. This graph does not represent a function.
Explanation:
The easiest way to say it is that this is not a function because it does not pass the vertical line test. This test takes all theoretical vertical lines that pass through a graph; if any vertical line intersects the graph more than once, the graph does not represent a function.
Another way to say it is that each input can correspond to only a single output. So, for each x value, there can be only one y value. It must be remembered that the reverse is not true; one output can correspond to more than one input (as in quadratic functions). This is not the graph of a function because at the input x=2, for example, the output y equals -6, -2, 2, and 6.
To revisit the vertical line test, the vertical line x=2 intersects the graph four times.
This is not the graph of a function.