It is a function.
The graph is an example of a Quadratic Function.
The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
To use the vertical-line test, imagine dragging a ruler held vertically across the
graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value.
The attached image is an example of a Vertical Line Test. If you repeat the same steps and draw vertical lines throughout the graph, it will produce the same results — that each vertical line crosses the graph once.
Therefore, the given parabola is a function.