The piecewise function is .

(a)

Graph :

Graph of the function  :

(b)

(i)

Find .

Observe the graph.

As  tends to  right hand side, the value of  approaches to .

.

(ii)

Find .

Observe the graph.

As  tends to  left hand side, the value of  approaches to .

.

(iii)

Find .

Observe the graph.

As  tends to  right hand side, the value of  approaches to .

.

As  tends to  left hand side, the value of  approaches to .

.

Left hand limit and right hand limit are not equal.

So  does not exist.

(iv)

Find .

Observe the graph.

As  tends to  right hand side, the value of  approaches to .

.

As  tends to  left hand side, the value of  approaches to .

.

Left hand limit and right hand limit are equal, so limit exist.

.

(a) Graph of the function  is

(b) (i) .

    (ii) .

    (iii)  does not exist.

    (iv) .