Question

What is an example of a function g(x) that is continuous for all values of x except x=-1, where it has a non removable discontinuity?

Answer 1

Use any piecewise defined function that has rules for `x < -1` and `x > -1` that are
(1) continuous, but that
(2) do not agree at `x=-1`.

Or use a function that is continuous everywhere axcept that is has one vertical asymptote. Translate left or right to place the asymptote at `x=-1`.