short answer: yes.
the definition of a function is a graphical relation in which each x value (input) has only one y value (output). if we use the vertical line test, we can see that each x value on this graph corresponds to one y value and one only. if a certain x value had more than one y value, then it wouldn’t be a function.
hope this helped, i tried to keep this concise but if you need a better explanation let me know :)
