Can someone help me with this question. With steps.

Question

Examine the continuity of the function

h(x)=

-x, if x<0
0, if x=0
x, if x>0

Answer 1

What would be discontinous at x=?

explain please

Answer 2

This is just h(x) = |x|
h is continuous at x=0, but

h' is discontinuous at x=0, since
h'(x) = -1 for x < 0
h'(x) = 1 for x > 0

Answer 3

Is there suppose to be calculations involved? :|