Question

What is the discontinuity of the function `f(x) = 1/x` ?

Answer 1

The discontinuity for `f(x)=1/x` is at `x=0`.

Discontinuities occur at values of x where the graph can't be evaluated. Since division by 0 is mathematically undefined, we can't plot a point for it on the graph of `1/x`, it represents a break in the graph.

This also means that in this case, there is actually a vertical asymptote with the equation `x=0`.