Questions: Question Watch Video Show Ex f(x) = - (x+1)^2 + 3 for -4 ≤ x < -1 - -6 for x = -1 - x + 4 for x > -1 Find f(-4)

Transcript text: Question Watch Video Show Ex \[ f(x)=\left\{\begin{array}{lll} -(x+1)^{2}+3 & \text { for } & -4 \leq x<-1 \\ -6 & \text { for } & x=-1 \\ x+4 & \text { for } & x>-1 \end{array}\right. \] Find $f(-4)$

Solution

Solution Steps

To find $ f(-4) $, we need to determine which piece of the piecewise function applies to $ x = -4 $. We then evaluate the corresponding expression at $ x = -4 $.

Solution Approach

Identify the correct piece of the piecewise function for $ x = -4 $.
Evaluate the expression for that piece at $ x = -4 $.

Step 1: Identify the Correct Piece of the Piecewise Function

The piecewise function is defined as: \[ f(x) = \begin{cases} -(x+1)^2 + 3 & \text{for} & -4 \leq x < -1 \\ -6 & \text{for} & x = -1 \\ x + 4 & \text{for} & x > -1 \end{cases} \] For $ x = -4 $, we use the first piece of the function: $ -(x+1)^2 + 3 $.

Step 2: Evaluate the Expression at $ x = -4 $

Substitute $ x = -4 $ into the expression: \[ f(-4) = -((-4) + 1)^2 + 3 \] Simplify the expression: \[ f(-4) = -(-3)^2 + 3 = -9 + 3 = -6 \]