Question

f(x) = \begin{cases} -x + 3 & \text{for } x leq -3 \\ -3x - 4 & \text{for } -3 < x leq 1 \\ -(x - 2)^2 + 5 & \text{for } x > 1 end{cases}

find f(-2)

Explanation:

Step1: Identify relevant function piece

Check that $-2$ satisfies $-3 < x \leq 1$, so use $f(x) = -3x - 4$.

Step2: Substitute $x=-2$ into the function

Substitute $x=-2$ into $-3x - 4$:

$$\begin{align*} f(-2) &= -3(-2) - 4 \end{align*}$$

Step3: Calculate the result

Compute the arithmetic:

$$\begin{align*} f(-2) &= 6 - 4 = 2 \end{align*}$$

Answer:

2