1. **State the problem:** We have a piecewise function $$k(x) = \begin{cases} \sqrt[3]{x+1} & \text{if } x < 8 \\ -8x + 1 & \text{if } 8 \leq x \leq 16 \\ x + 3 & \text{if } x > 16 \end{cases}$$ We want to find the value of $k(x)$ when $x = 8$. 2. **Identify which piece to use:** Since $x=8$ falls in the interval $8 \leq x \leq 16$, we use the middle piece: $$k(x) = -8x + 1$$ 3. **Calculate $k(8)$:** Substitute $x=8$ into the formula: $$k(8) = -8(8) + 1 = -64 + 1 = -63$$ 4. **Interpretation:** The value of the function at $x=8$ is $-63$. This matches the graph segment starting at approximately $(8, -63)$. **Final answer:** $$k(8) = -63$$