As you said on the question page, we will use the vertical line test to see if it is a function or not.
But why do we use the vertical line test?
Well, all functions have an x-value and just one corresponding y-value, if you have a graph and for one single x-value you have more than one y-value it means it is not a function but a relation. So that is why we use the vertical line test, to figure how many y-values are corresponding to a single x-value. Let's draw the graph and do the test as follows:
As we can see above, for all vertical red lines we draw for each x-value, the red lines touched just at one point on the function line, which means there is just one y corresponding value for each x-value. We can do as many vertical lines as we need and we will always have the same result for our function. So the final answer is: The graph represents a function.
As we could see above, for each red line, it just crosses the function once (at one single point) but let's take a look at a different situation, where we do not have a function:
As we can see above, it is represented a circle in blue. So, for a vertical line test, we can draw several red vertical lines and we can see it crosses our "possible function" (blue circle) at two points, which means it is not a function.