The function is , where is the number of liters of 4-molar solution added.

(a).

Find .

Substitute in .

.

The function is defined for .

Find if exists.

Construct a table that shows the values of for -values approaching from the left and from the right. 

Observe the table.

As tends to from the left and from the right , approaches to .

.

Observe above two conditions,

Since , is continuous at .

 (b).

The function .

Domain of above rational function is all real numbers except .

is undefined.

 The function is discontinues at .

Construct a table that shows the values of for -values approaching from the left and from the right. 

Observe the table:

As tends  to   from the left approaches .

As tends to from the right, approaches to .

and .

Since, is discontinuous at .

Observe above two conditions,

does not exist and is undefined.

Because and , has an infinite discontinuity at .

The discontinuity has no effect on the concentration of the mixture because the model is only valid for non-negative values of .

(c).

Graph of the function :

 Observe the graph:

As tends  to   from the left approaches .

As tends to from the right, approaches to .

has an infinite discontinuity at .

(a). is continuous at .

(b).  The function is discontinues at   and has infinite discontinuity at .

(c). Graph of the function :

.