A salesperson has 50 shirts to sell and must sell a minimum of 20 shirts. The salesperson sells the shirts for $35 each. The amount of money the salesperson makes for selling x shirts is represented by a function. f (x) = 35x What is the practical range of the function?

Answer: all multiples of 35 between 700 and 1750, inclusive.

Justification:

The range of the function f (x) = 35 x is all the real numbers (zero, positives and negatives). But here you have these restrictions about the domain (this is the possible values of x):

1) x is an integer number (the number of shirts)

2) x is greater or equal than 20

3) x is less or equal than 50

Then, you have to find f (x) for the limit values

f (20) = 35*20 = 700

f (50) = 35*50 = 1750

You can see that f (x) is the set 35*20, 35*21, 35*22, 35*23, ... until 35*50, i. e. all the multiples of 35 between 700 and 1750, inclusive.

The "range" is the possible values of y, so if x = 35, then y = 20-50.

Since the salesperson must sell 20 shirts, the range starts at 20. But since he only has 50 shirts, he can't sell more than 50. So, the range ends at 50.