approch 0 from above and -infty as you approach 0 from below, so near 0
a small change in x cn result in a large change in y, hence this is
discontinuous at x=0.
For you other example if you change x to x+e, y changes from x*2 to
x*2+e*2, and as e is small so is e*2.
Note by convention in ASCII (plain text) * denotes multiplication. If you
meant x squared you should use x^2. In this case y changes from x^2 to
(x+e)^2 = x^2 + 2e x + e^2, and if e is small enough 2e x+e^2 is also