What is function which is has irremovable discontinuity at x-2 removable discontinuity at x2 and continuous at other points?

"Removable discontinuity" means the function is not defined at that point (it has a "hole"), but by changing the function definition at that single point, defining it to be certain value, it becomes continuous. "Irremovable discontinuity" means the function makes a sudden jump at that point. There are infinitely many functions like that; for example, you can set the function to be:

f(x) is undefined at x = -2

f(x) = 0 for x < 2 (except for x = -2)

f(x) = 1 for x > 2