Question

create a graph that has two discontinuities, one removable and one non removable?

Answer 1

a removable discontiuity can be "removed" to make the function continuous. The limit exists at that point but is not equal to the value of the function.
f(x)= x x<1
0 x=1
2x -1 1<x<3
3 x=3
1 x>3

Answer 2

the first discont. at x=1 is removable, and at x=3 we have a non-removable discont.