the function that represents the average cost per person, including transportation, to a museum is $y =…

the function that represents the average cost per person, including transportation, to a museum is $y = \\frac{25 + 8x}{x}$. which statement is true about the graph of the function?\nthe horizontal asymptote $y = 0$ means the cost approaches zero as the number of people increases.\nthe horizontal asymptote $y = 8$ means the average cost approaches $8 as the number of people increases.\nthe vertical asymptote $x = 0$ means the cost approaches zero as the number of people increases.\nthe vertical asymptote $x = 8$ means the cost approaches zero as the number of people increases.

the function that represents the average cost per person, including transportation, to a museum is $y = \\frac{25 + 8x}{x}$. which statement is true about the graph of the function?\nthe horizontal asymptote $y = 0$ means the cost approaches zero as the number of people increases.\nthe horizontal asymptote $y = 8$ means the average cost approaches $8 as the number of people increases.\nthe vertical asymptote $x = 0$ means the cost approaches zero as the number of people increases.\nthe vertical asymptote $x = 8$ means the cost approaches zero as the number of people increases.

Answer

Explanation:

Step1: Rewrite the function

We have $y=\frac{25 + 8x}{x}=\frac{25}{x}+8$.

Step2: Analyze horizontal asymptote

As $x\to\pm\infty$, $\frac{25}{x}\to0$. So $y\to8$. The horizontal asymptote is $y = 8$, which means the average - cost approaches $$8$ as the number of people ($x$) increases.

Step3: Analyze vertical asymptote

The function $y=\frac{25 + 8x}{x}$ is undefined when $x = 0$. So the vertical asymptote is $x=0$. When $x$ approaches $0$ (but $x\neq0$), the value of the function goes to $\pm\infty$.

Answer:

The horizontal asymptote $y = 8$ means the average cost approaches $$8$ as the number of people increases.