Question

assume that you are given the graph of a function explain briefly how do you know that the graph really represents a function?

Answer 1

IS this calculus or just basic geometry?

Answer 2

its for a college algebra class

Answer 3

Lets say you have knowing these you can say that it is
f(x) = (x+3)(x+1)(x-1) expand the second 2 parenthesis this is easier
f(x) = (x+3)(x^2-1)
f(x) = x^3+3x^2-x-3

See how I found the function using just the given graph?