how do you know if a graph has an inverse?

Question

all i know is something about the horizontal rule or something..

Answer 1

The horizontal line rule shows you whether a graph is a 'function' meaning only one x value corresponds to one y value. The inverse function simply means that you put a one over the function, for instance for the equation y=x the inverse is 1/x

Answer 2

Graphs don't exactly have inverses. Graphs represent functions, which may or may not have inverses.

A function f has an inverse if and only if there is never a case when f(a) = f(b) for a,b not equal to each other. That's the same thing as saying there never is a case that a horizontal line intersects the graph of the function in more than one place

To see why those are the same thing, note that the equation of a horizontal line is just y = c. So if it cuts the graph in two places, that means there are two different x with f(x) = c.