Final answer:
The cost function C(x) represents the total cost of producing x t-shirts. It is given by C(x) = 7x + 45, where 7x represents the variable cost and 45 represents the fixed cost for the design fee.
Step-by-step explanation:
The subject of this question is Mathematics. The cost function is a mathematical representation of the total cost of producing a certain quantity of t-shirts. In this case, the cost function C(x) is given by C(x) = 7x + 45, where x represents the number of t-shirts produced. The term 7x represents the variable cost, which is $7 per t-shirt, and the constant 45 represents the fixed cost for the design fee. By plugging in different values for x, you can calculate the total cost of producing a specific quantity of t-shirts.