No, the piecewise graph is NOT a function because it does NOT pass the vertical line test.
The vertical line test is where we try to pass a line through more than one point on the curve. If it is not possible to do this, then the graph is said to "pass the vertical line test".
In this case, the given graph fails the vertical line test. Look at something like x = -2. We can draw a vertical line through here to pass through more than one point. One point is on the upside-down V shape, and the other point is on the parabolic shape. Plugging x = -2 into this leads to more than one y outputs.
A function is only possible if any valid x input (from the domain) leads to exactly one output y value (in the range).
