Question

question
$f(x)=\

$$\begin{cases}-x + 3&\\text{for }x\\leq - 3\\\\-3x - 4&\\text{for }-3 < x\\leq1\\\\-(x - 2)^2+5&\\text{for }x > 1\\end{cases}$$

$
find $f(-2)$
answer attempt 1 out of 2
undefined

Explanation:

Step1: Determine the applicable piece

We need to find \( f(-2) \). First, check which interval \( -2 \) belongs to. The intervals are \( x \leq -3 \), \( -3 < x \leq 1 \), and \( x > 1 \). Since \( -3 < -2 \leq 1 \), we use the piece \( f(x)= -3x - 4 \).

Step2: Substitute \( x = -2 \) into the piece

Substitute \( x=-2 \) into \( -3x - 4 \):
\( f(-2)=-3(-2)-4 \)
First, calculate \( -3(-2)=6 \), then \( 6 - 4 = 2 \).

Answer:

\( 2 \)