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) = (200+3.10x) / (X) Which statement is true?

A. 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.

B. The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

C. 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.

D. The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

Question

Mathematics

Ocean

7 October, 20:27

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) = (200+3.10x) / (X) Which statement is true?

A. 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.

B. The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

C. 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.

D. The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

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Answers (1)

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Moshe Rasmussen · Answer 1

Given:

f (x) = (200 + 3.10x) / x

Finding the horizontal asymptote

1) put equation in y form: y = 200 + 3.10x / x

2) remove everything except the terms with the biggest exponents of x

y = 3.10x / x

3) remove x to recognize the horizontal asymptote: y = 3.10

Finding the vertical asymptote

1) set the denominator to be equal to 0 and solve for x

f (x) = 200 + 3.10x / x

x = 0

f (x) = 200 + 3.10 x / 0

My answer is:

A. 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.