Graph of rational functions are smooth but not continuous.

Consider a rational function .

Graph : 

Graph the function .

Observe the above graph : 

Since the graph has no corners, the graph is smooth.

The graph is discontinuous at .

Thus, the graph of is smooth but not continuous.

Graph of absolute value functions are continuous but not smooth.

Consider a absolute value function .

Graph : 

Graph the function .

Observe the above graph : 

Since the graph has corner at , the graph is not smooth.

The graph is continuous.

Thus, the graph of is continuous but not smooth.

The graph of is smooth but not continuous.

The graph of is continuous but not smooth.