A function is a relation that gives each element of X, the input, exactly one element of Y, the output. An example of this: The points (x,y), (x+1, y), (x+2, y+1), etc. create a function. The points (x,y), (x, y+1) are not a function because one value of x becomes two values of y. In short, if a value of x gives two values of y, the equation is not a function.