Answer
a) $C(m)=\frac{800}{m-5}$
b) The cost person who is not graduating is $\$20$.
c) Domain: $10\leq m\leq 50$
Range: $17.78\leq C(m)\leq 160$
Work Step by Step
a) Let $C(m)$ be cost per member who attends the math club party and $m$ be the total number of members attending (including the 5 graduates). Then\begin{equation}
\begin{aligned}
C(m)&=\frac{500+300}{m-5}\\ &= \frac{800}{m-5}.
\end{aligned}
\end{equation} b) The cost person who is not graduating is $\$20$. \begin{equation}
\begin{aligned}
C(45)&=\frac{800}{45-5} \\
&= 20\\
\end{aligned}
\end{equation} c) The function requires that $m> 5$. Take the minimum number of member to be $m= 10$. Then
\begin{equation}
\begin{aligned} C(10)&=\frac{800}{10-5}=160\\C(50)&= \frac{800}{50-5}= 17.78
\end{aligned}\end{equation}A reasonable domain and range of the function is:
$$
\begin{aligned}
\textbf{Domain: }&10\leq m\leq 50\\
\textbf{Range: }&17.78\leq C(m)\leq 160 \\
\end{aligned}
$$
