The y-intercept of a graph (or function, `y` = `f`(`x`)) is where the graph intercepts the y-axis.

The y-axis is given by the equation `x` = 0, so the y-intercept of a function is the solution to the simultaneous equations `y` = `f`(`x`) and `x` = 0, or, `x` = 0 and `y` = `f`(0) - also written (0, `f`(0)).

It is possible that a function is undefined at zero (e.g. `f`(`x`) = 1 / `x`), in which case there is no y-intercept; if the function *is* defined at zero then there is one intercept. There can never be more than one.

C-Dawg has (correctly) pointed out to me that a relation (which frequently gets confused for a function) can have more than one y-intercept, and that parametric functions sometimes used for describing graphs (e.g. `x`(`θ`) = cos(`θ`), `y`(`θ`) = sin(`θ`)) can have more than one y-intercept too. In all cases, to find the y-intercept(s), solve whatever equations are given with the constraint `x` = 0.