the cost $ C, of producing x units of a product is given by the function:

Question

 The cost $ C, of producing x units of a product is given by the function:  C=4000+2x, up to a cost of $12,000.

 

Find the domain and range

Answer 1

Domain is the list of inputs or x-values that make sense in the context of the function. Since this function is talking about the production of items, we can safely assume that x cannot be negative and that it cannot be a fraction/decimal value. We also cannot produce past a cost of $12000.
Solving the following equation allows us to find that upper limit:

12000 = 4000 + 2x
8000 = 2x
x = 4000


Therefore, the domain would be: {0, 1, 2, 3, ..., 4000}

Range is the list of outputs or C-values that make sense in the context of the function. Since this function is talking about the cost of producing items, we can look at what it costs to produce 0 items, 1 item, 2, 3, and so on to see a pattern. We also know that the upper limit to the cost is $12000.

Therefore, the range would be: {4000, 4002, 4004, 4006, ... , 12000}