No, the graph is a relation and not a function.
Functions and relation
A function is a relation whereby each set of element X(domain) is matched to a another set Y(codomain). The domain is the set of all possible input for the function and the codomain is the set of all possible output values. A relation is a set of orderly pairs that has a input and output values.
On a graph, the set of values on the x-axis are the domain and the y-values are the range. To determine if a graph is a function, the graph must pass the vertical line test.
The vertical line test is a straight vertical line draw on the line of the graph, that if the vertical intersects the graph line more than one point, then that graph is not regarded as a function but it is a relation.
From the graph in the given image, we can conclude that the graph is not a function but a relation because it does not pass the vertical line test.