1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} -x^2 + 10 & \text{if } -4 \leq x < 4 \\ 6 - 3x & \text{if } x \geq 4 \end{cases}$$ We need to graph this function and determine if it is continuous. 2. **Graph the function:** - For $-4 \leq x < 4$, the function is $f(x) = -x^2 + 10$, a downward-opening parabola shifted up by 10. - For $x \geq 4$, the function is $f(x) = 6 - 3x$, a linear function with slope $-3$. 3. **Check continuity at $x=4$:** - Calculate the left-hand limit: $$\lim_{x \to 4^-} f(x) = -4^2 + 10 = -16 + 10 = -6$$ - Calculate the right-hand limit and function value at $x=4$: $$f(4) = 6 - 3 \times 4 = 6 - 12 = -6$$ 4. **Conclusion:** Since the left-hand limit, right-hand limit, and function value at $x=4$ are all equal to $-6$, the function is continuous at $x=4$. **Final answer:** The function is continuous on its entire domain.