You can use the vertical line test to determine if the graph is a function.
A function must: for every x value have only one y value.
Vertical line test: if you draw a bunch of vertical lines each line only touches the graph once. So a circle would not be a function, or a horizontally facing parabola, etc... Remember, if you draw a vertical line "|" and it touches the graph more than once at any point then it is not a function.
Now take a look at the graph in the question. In this graph if we do the vertical line test there are no place where a vertical line touches the graph twice so this graph is indeed a function.
