1. **State the problem:** We need to find the values of the piecewise function $$f(x) = \begin{cases} x + 1 & \text{if } x \leq -1 \\ x^2 & \text{if } x > -1 \end{cases}$$ at $x = -3$, $x = 0$, and $x = 2$. 2. **Understand the function:** The function has two parts: - For $x \leq -1$, use $f(x) = x + 1$. - For $x > -1$, use $f(x) = x^2$. 3. **Calculate $f(-3)$:** Since $-3 \leq -1$, use $f(x) = x + 1$. $$f(-3) = -3 + 1 = -2$$ 4. **Calculate $f(0)$:** Since $0 > -1$, use $f(x) = x^2$. $$f(0) = 0^2 = 0$$ 5. **Calculate $f(2)$:** Since $2 > -1$, use $f(x) = x^2$. $$f(2) = 2^2 = 4$$ **Final answers:** - $f(-3) = -2$ - $f(0) = 0$ - $f(2) = 4$