(a)

The initial investment is .

The cost each shirt is .

First write the linear equation.

Cost = variable cost + fixed cost.

Fixed cost is and the variable cost is per T-shirt.

The cost function for producing shirts is .

The function to represent the average cost per shirt as a function of the number of shirts sold is .

The function is .

 (b)

In this case represents the number of  T-shirts, so graph of the function is valid only positive values of .

Graph of the function :

(c)

Observe the graph:

End behavoiur of the graph is .

As tends to , approches .

Therefore, the average cost approches as the number of  T-shirts sales increases.

(a) The function is .

(b) Graph of the function :

(c) The average cost approches as the number of  T-shirts sales increases.