1. The problem is to graph the piecewise function: $$y=\begin{cases}2x & 0 \leq x \leq 4 \\ 10 & 4 < x \leq 8\end{cases}$$ 2. This function has two parts: a linear part $y=2x$ from $x=0$ to $x=4$, and a constant part $y=10$ from $x=4$ to $x=8$. 3. At $x=4$, the value from the first part is $y=2\times4=8$, so the graph has a filled circle at $(4,8)$ for the first part. 4. For the second part, $y=10$ for $4 < x \leq 8$, so the graph is a horizontal line at $y=10$ starting just after $x=4$ (open circle at $(4,10)$) and ending with a filled circle at $(8,10)$. 5. The graph shows a line increasing from $(0,0)$ to $(4,8)$, then jumps to $y=10$ for $4 < x \leq 8$. 6. This matches the description: a vertical axis with cost values including 10 and 8, a horizontal segment from $x=4$ to $x=8$ at $y=10$ with an open circle at $x=4$ and filled circle at $x=8$. Final answer: The graph is the piecewise function given above.