The piecewise function is  .

(a) 

All possible values of for which the function is mathematically correct is the domain of a function. 

The domain set is

Domain in interval notation .

(b) Find the intercepts.

Find the -intercept by substituting .

If then the function is .

Substiute in above function.

The value of which is not to be considered because .

If then the function is .

Substitute in above function.

The -intercept is .

Find the -intercept by substituting .

Substitute in .

The functions ,  are not defined at .

The -intercept is .

(c)

Draw the table of different values of for .

	\ \	\ \
	\ \	\ \
	\ \	\ \

	\ \	\ \
	\ \	\ \
	\ \	\ \

 Graph:

1). Draw a coordinate plane.

2). Plot the points found in the table and connect the plotted points

3). Label the intercept points.

(d)

All possible values of is the range of a function.

Observe the graph: The range of function is .

The range in interval notation .

(e)

The function is discontinuous at .

(a) Domain in interval notation .

(b) Intercepts are and .

(c) Graph of the function :

(d) The range in interval notation .

(e) The function is discontinuous at .