For every point x0 in the domain of a function f, the intersection of the graph of f with the vertical line x = x0 will be the single point (x0,f(x0)).
In this demo, we see how a vertical line intersecting a function graph in the plane creates a slice which is the point (x0, f(x0)). Try changing x0 and the expression for f(x).
ExercisesWhat would happen if we sliced a function graph in the plane with a line that wasn't vertical? Would the slice still always be a single point? Give a proof or a counterexample.