Concept of a Function
Here is another way to understand the concept of a function as I can best define it. We know that y is a function of x when every x value has one unique y value. For example, if these points were in a function: (0,0) (1,0) (2,6), this would be a function because every x value has a unique y value.
However, if you had these points in a function: (0,0) (2,5) (2,10) (3,2), this would not be a function because the x value of 2 has two different y values, 5 and 10.
To determine if a graph is a function, it has to pass the "vertical line test". This is done by simple moving an imaginary line parallel to the y-axis across the entire graph. As long as this line only touches the graph at 1 point at all times, then the function is legitimate.