Question

10. 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.

Answer 1

Answer:

Option 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.

Step-by-step explanation:

Given : 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 $f(x)=\frac{200+3.10x}{x}$

To find : Which statement is true?

Solution :

The company is tracking its average cost to make x units using $f(x)=\frac{200+3.10x}{x}$

As the given average cost equation is of hyperbola.

Its vertical asymptote is when we equating denominator to zero,

i.e, x=0 ⇒ y axis.

Its horizontal asymptote is the leading coefficient of numerator divided by leading coefficient of denominator,

i.e, $y=\dfrac{3.10}{1}=3.10$

As $x\rightarrow \infty, y=3.10$

Therefore, Option a is correct.

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.

Answer 2

Using asymptote concepts, it is found that the true statement is given by:

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.

What are the asymptotes of a function f(x)?

• The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

• The horizontal asymptote is the value of f(x) as x goes to infinity.

In this problem, the function for the average cost of producing x units is given by:

$f(x) = \frac{200 + 3.1x}{x}$

Hence:

• The vertical asymptote is at x = 0, which means that when 0 units are produced, the function for the average cost per unit is not defined.

For the horizontal asymptote, we have that:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{200 + 3.1x}{x} = \lim_{x \rightarrow \infty} \frac{3.1x}{x} = \lim_{x \rightarrow \infty} 3.1 = 3.1$

Thus, option A is correct.

You can learn more about horizontal and vertical asymptotes at https://brainly.com/question/16948935