continuous just means that the graph is connected.
e.g. if you have a piece meal function:
x - 1 for x> 0
and x for x< 0
There is discontinuity at x =0, as there are no values for x = 0.
also, if you have a hyperbola like y = 1/x. It is discontinuous when x = 0, as there is an asymptote there.
to find continous/discontinous points:
continous: occurs when there is no gap in the curve. Find the values for which x cannot be equal to. e.g. x -2 >> 0. x must be greater or equal to 2. and hence, the curve is continuous when x is >>2.