Question

What is the difference between a vertical asymptote and a removable discontinuity?

Answer 1

A removable discontinuity causes a hole in the graph.

`y = x^2/x` looks like the line `y=x`, except for the hole at `(0,0)`

`y = (x^3-2x)/(x-2)` looks like the parabola `y = x^2` except it has a hole at `(2,4)`

A vertical asymptote is a vertical line that a graph approaches, line the line `x=1` for the graph of `y=x/(x-1)`