Question

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using f (x) = StartFraction 200 + 3.10 x Over x EndFraction. Which statement is true?
The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

Answer 1

The first statement is true.

Reason: f(x) = (200 + 3.10x)/x = 3.10 + 200/x, so as x → ∞ the 200/x term → 0 and f(x) → 3.10. (x = 0 is a vertical asymptote and f(x) → ∞ as x → 0+, not 0.)