Observe the graph of the function.

(a) 

We can observe from the graph that  exists.

The black dot indicates the value of the function at .

(b) 

We can observe from the graph that  does not exists.

As  approaches to  from the left side then  approaches to  approximately.

As  approaches to  from the right side then  approaches to  approximately.

Since the left hand limit and right hand limit are not equal, limit does not exist.

 does not exist.

(c) 

We can observe from the graph that  does not exists.

The hollow dot indicates that value of the function does not exist at .

 is undefined.

(d) 

We can observe from the graph that  exists.

As  approaches to  then  approaches to .

Therefore .

(a) 

(b)  does not exist.

(c)  is undefined.

(d) .