a certain company has a fixed cost of $200 per day. it costs the company $3.10 per unit to make its…

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

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

Explanation:

Step1: Analyze the average - cost function

The average - cost function is $f(x)=\frac{200 + 3.10x}{x}=\frac{200}{x}+3.10$.

Step2: Find the horizontal asymptote

As $x\to\infty$, $\lim_{x\to\infty}\frac{200}{x}=0$. So, $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}(\frac{200}{x}+3.10)=3.10$. The horizontal asymptote of the function $y = f(x)$ is $y = 3.10$. This means that as the number of units $x$ produced increases, the average cost per unit will approach $$3.10$.

Step3: Analyze the vertical asymptote

The function $f(x)=\frac{200 + 3.10x}{x}$ is undefined when $x = 0$. The vertical asymptote is $x = 0$, but it has nothing to do with the average - cost approaching a certain value as the number of units produced increases.

Answer:

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.