Graph the piecewise-defined function.

We have to graph the piecewise-defined function h(x) which is given as:

h(x)=  x^3   '  if x <0

   and  √x   ' if x ≥ 0.

We could clearly see that the graph of a function is continuous since the left hand limit(L.H.L) of the function is equal to the right hand limit(RH.L.) is equal to the value of the function at x=0.

L.H.L=R.H.L=h(0)=0

Also the graph of the function h(x) in the region (-∞,) is a graph of the cubic function x^3 and the graph of the function h(x) in the region [0,∞) is the graph of the square root function √x.