a function is a graph where you can't cut the curve in more than one place with a vertical line. It's the "vertical line test."
for example, y=x^2 is a function, f(x) = x^2, since any vertical line will only intersect the curve in one point
but x=y^2 is not a function, since any vertical line will cut the curve in 2 points. It's a "relation" but not a "function"