The function is .

Rewrite the function .

(a)

The range of , where .

For , the function is .

Graph of the function :

For , the function is .

Graph of the function :

.

For , the function is .

Graph of the function :

.

For , the function is .

Graph of the function :

.

For , the function is .

Graph of the function :

.

 For , the function is .

Graph of the function :

 .

 (b)

Observe the graphs of the above functions,

Function	Domain	Range

(c)

Symmetry of each function:

Observe that the odd functions have origin symmetry, because is equivalent to , is equivalent to and is equivalent to .

Even functions have -axis symmetry  is equivalent to , is equivalent to and is equivalent to .

Symmetry of the functions:

Function	-axis	-axis	Origin
	No	No	Yes
	No	Yes	No
	No	No	Yes
	No	Yes	No
	No	No	Yes
	No	Yes	No

 (d)

The function .

Since is an odd number, the domain and range of the function is  .

Because is equivalent to , the function is symmetric with respect to the origin.

(a) Graphs of six functions.

, ,

,,

,.

(b)

Function	Domain	Range

(c) Odd functions symmetry with respect to the origin.

Even functions symmetry with respect to the -axis.

(d) Domain and range of is .

Symmetry of is respect to the origin.