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: Simplify 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 $y = 8$. This means that as the number of people $x$ increases, the average cost per person approaches $\$8$.

Step3: Analyze vertical asymptote

The function $y=\frac{25 + 8x}{x}$ is undefined when $x = 0$. So the vertical asymptote is $x = 0$.

Answer:

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