1. **State the problem:** We have a piecewise function defined as $$f(x) = \begin{cases} -\frac{x}{2} + 6 & \text{for } -10 \leq x \leq -4 \\ \frac{10}{3} & \text{for } -4 < x < 3 \\ \frac{10}{x} & \text{for } x \geq 3 \end{cases}$$ 2. **Understand the function:** This function has three parts, each valid on a different interval of $x$. 3. **Evaluate or analyze:** To understand or graph this function, evaluate each piece on its domain. 4. **Example evaluations:** - For $x = -6$ (in $-10 \leq x \leq -4$), $$f(-6) = -\frac{-6}{2} + 6 = 3 + 6 = 9$$ - For $x = 0$ (in $-4 < x < 3$), $$f(0) = \frac{10}{3} \approx 3.333$$ - For $x = 5$ (in $x \geq 3$), $$f(5) = \frac{10}{5} = 2$$ 5. **Summary:** The function is linear on $[-10,-4]$, constant on $(-4,3)$, and rational on $[3,\infty)$. This completes the description and evaluation of the piecewise function.