Questions: Consider the following piecewise-defined function. f(x) = - x + 2 if x ≤ 1 - 1/3x - 3 if x > 1 Step 3 of 3: Evaluate this function at x = -2. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". f(-2) =

$Consider the following piecewise-defined function. f(x) = - x + 2 if x ≤ 1 - 1/3x - 3 if x > 1 Step 3 of 3: Evaluate this function at x = -2. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". f(-2) =$

Transcript text: Consider the following piecewise-defined function. $f(x) = \begin{cases} -x + 2 & \text{if } x \leq 1 \\ -\frac{1}{3}x - 3 & \text{if } x > 1 \end{cases}$ Step 3 of 3: Evaluate this function at x = -2. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". $f(-2) = \square$ $\bigcirc$ Undefined

Solution

Solution Steps

To evaluate the piecewise function at $ x = -2 $, we need to determine which condition $ x = -2 $ satisfies. Since $-2 \leq 1$, we use the first piece of the function, $ f(x) = -x + 2 $. Substitute $-2$ into this expression to find $ f(-2) $.

Step 1: Determine the Applicable Piece of the Function

To evaluate the function $ f(x) $ at $ x = -2 $, we first identify which piece of the piecewise function to use. Since $ -2 \leq 1 $, we use the first piece of the function:

\[ f(x) = -x + 2 \]

Step 2: Substitute the Value into the Function

Next, we substitute $ x = -2 $ into the selected piece of the function:

\[ f(-2) = -(-2) + 2 \]

Step 3: Simplify the Expression

Now, we simplify the expression:

\[ f(-2) = 2 + 2 = 4 \]