Question

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?
the horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.
the horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.
the vertical asymptote x = 0 means the cost approaches zero as the number of people increases.
the vertical asymptote x = 8 means the cost approaches zero as the number of people increases.

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 as the number of people ($x$) increases, the average cost ($y$) approaches $\$8$.

Step3: Analyze vertical asymptote

The function $y=\frac{25 + 8x}{x}$ is undefined when $x = 0$. The vertical asymptote is $x=0$, which represents a non - physical situation (division by zero) and has nothing to do with the cost approaching zero as the number of people increases.

Answer:

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