Question

Give an example of a function with at least one removable and one non-removable discontinuity (that has not been discussed in any lesson). Explain where the discontinuities occur and provide a justification for your reasoning. You may use a graph of the function to help explain your answers

Answer 1

\[\huge f(x)=\frac{(x+1)}{(x+1)(x-2)} \]

this function has a removable discontinuity at x=-1, because the common factors on the top and bottom will cancell. this will create a hole on your graph.
the nonremovable discontinuity occurs at x=2 because there is a vertical asymptote there.