In order to be a function, every value of x can have only one corresponding value of y.
If a value of x has two or more values of y, so the graph is not a function.
Looking at the graph, every value of x has only one corresponding value of y, therefore the graph is a function.
Another way of checking if the graph is a function is by imagining vertical lines along the graph. If a line intersects the graph more than one time, so the graph is not a function
If every vertical line intersects the graph only once, so the graph is a function.
Every red line intersects the graph only once (yellow dots), so the graph is a function.
An example where the graph is not a function is:
There are some red lines that have two or more intersects (in this case, two intersects), therefore the graph is not a function.