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.