1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} x^2 + 2 & \text{if } x < 1 \\ x - 5 & \text{if } x \geq 1 \end{cases}$$ We need to find the values of $f(-2)$ and $f(3)$. 2. **Evaluate $f(-2)$:** Since $-2 < 1$, we use the first part of the function: $$f(-2) = (-2)^2 + 2 = 4 + 2 = 6$$ 3. **Evaluate $f(3)$:** Since $3 \geq 1$, we use the second part of the function: $$f(3) = 3 - 5 = -2$$ 4. **Final answers:** $$f(-2) = 6$$ $$f(3) = -2$$ These values come directly from substituting into the correct piece of the piecewise function based on the input value.