Question

the equation of the piecewise function f(x) is below. what is the value of f(-2)?

f(x) = \

$$\begin{cases} -x^2, & x < -2 \\\\ 3, & -2 \\leq x < 0 \\\\ x + 2, & x \\geq 0 \\end{cases}$$

\bigcirc \\ f(-2) = -6
\bigcirc \\ f(-2) = -4
\bigcirc \\ f(-2) = 0
\bigcirc \\ f(-2) = 3

Explanation:

Step1: Determine the domain for \( x = -2 \)

We need to find which piece of the piecewise function \( f(x) \) applies when \( x = -2 \). Looking at the intervals:

• The first piece is for \( x < -2 \), but \( -2 \) is not less than \( -2 \).
• The second piece is for \( -2 \leq x < 0 \). Since \( -2 \) satisfies \( -2 \leq x < 0 \) (because \( -2 = -2 \) and \( -2 < 0 \)), we use this piece.

Step2: Evaluate the function at \( x = -2 \)

The second piece of the function is \( f(x) = 3 \) for \( -2 \leq x < 0 \). So when \( x = -2 \), we substitute into this piece:
\( f(-2) = 3 \)

Answer:

\( f(-2) = 3 \) (corresponding to the option: \( f(-2) = 3 \))