Question

Give an example of a function with both a removable and a non-removable discontinuity.

Answer 1

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Answer 2

\[\Large y=\frac{x^2-4}{x-2}\]We could simplify this function a bit,\[\Large y=\frac{(x-2)(x+2)}{x-2}\]Which simplifies to,\[\Large y=x+2\]This represents a straight line if we were to graph it.
But we still can't use the point x=2 because it causes a zero in the denominator of the original form.

So this is an example of a `removable discontinuity`.

Answer 3

If you're asked to come up with an example, the easiest thing to do is just make a piece-wise function.So for this function, we would graph y=x in all places except x=1.
At x=2, the function gives us y=2.