No, the graph shown is not a graph of a function.
Work Step by Step
We can use the vertical line test to determine if the graph is a graph of a function. If we add a vertical line $x=0$ to the graph, it will intersect the existing graph twice. Therefore, this cannot be a graph of a function, because x-values in this relationship correspond to more than 1 y-coordinate. A function is a relation in which each first component in the ordered pairs corresponds to exactly one second component.