- Question: Write a linear function
C(x) giving the total cost of producing x T-shirts. Remember to take
the start-up cost into account.
Answer: C(x) = 450 + 5.5 x (total cost in
- Question: Write a rational function A(x) giving
the average cost of producing x T-shirts.
|C(x) ||450 + 5.5 x|
| A(x) = ||-------- = ||------------------|
- Question: What is the domain of A(x) in the
context of the problem? Explain.
Answer: Domain is x > 0. Since x represents the
number of shirts produced, only non-negative values make sense. We have
to exclude x = 0 since A(x) is undefined for x = 0.
- Question: Does A(x) have a vertical asymptote? If
so what is its equation?
Answer: The vertical asymptote is x = 0.
- Question: Find the horizontal asymptote for A(x).
What meaning does this value have in the context of the problem?
Answer: The horizontal asymptote is y = 5.5. As
the number of shirts produced increases, the start-up costs are "spread
out" over a larger number of shirts. To see this mathematically, divide
each term in the numerator by x: A(x) = 450/x + (5.5 x)/x = 450/x +
As x increases without bound, 450/x approaches zero (becomes
negligible). Thus the average cost approaches, but never reaches $5.50