1. **Statement of the problem:** Calculate the values of the piecewise function $$f(x) = \begin{cases} x+3 & \text{if } x \leq 0 \\ x^2 - 2 & \text{if } 0 < x \leq 5 \\ 2x + 4 & \text{if } x > 5 \end{cases}$$ for $$x = -2, 2, 8$$. 2. **Recall the definition of piecewise function:** Choose the formula corresponding to the interval where the value of $$x$$ lies. 3. **Calculate $$f(-2)$$:** Since $$-2 \leq 0$$, use $$f(x) = x + 3$$. $$f(-2) = -2 + 3 = 1$$ 4. **Calculate $$f(2)$$:** Since $$0 < 2 \leq 5$$, use $$f(x) = x^2 - 2$$. $$f(2) = 2^2 - 2 = 4 - 2 = 2$$ 5. **Calculate $$f(8)$$:** Since $$8 > 5$$, use $$f(x) = 2x + 4$$. $$f(8) = 2 \times 8 + 4 = 16 + 4 = 20$$ **Final answer:** $$f(-2) = 1, \quad f(2) = 2, \quad f(8) = 20$$