The x-intercept of a graph (or function) is where the graph intercepts the x-axis.

The x-axis is given by the equation `y`=0, so the x-intercepts are the solutions to the simultaneous equations `y`=`f`(`x`) and `y`=0, or, `x`=`f`^{-1}(0) and `y`=0 - also written (`f`^{-1}(0), 0).

It is possible a function has no x-intercepts, it is possible it has one, it is possible it has many. For example, `f`(`x`) = `x`^{2} + 1 has no x-intercepts, `f`(`x`) = `x`^{2} has one x-intercept (at 0), `f`(`x`) = `x`^{2} - 1 has two intercepts (at -1 and 1), `f`(`x`) = `x` - ⌊`x`⌋ has an infinite number of x-intercepts (at each integer).