What is the value of \( f(-4) \) in the piecewise function?

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

(Note: Make sure the intervals make sense and check if \( x = -4 \) falls within one of the specified intervals.)

We first need to pick the correct piece to use. In this case, we will use f(x) = -x-5 because -5<=-4.
Then, we use direct substitution: f(-4) = -(-4) - 5 f(-4) = -1

Answered by chipperrider | 2024-06-10

The value for f(-4) in the piecewise function is -1 ;

Answered by ezequielburela | 2024-06-12

The value of f ( − 4 ) in the piecewise function is − 1 . This is calculated by using the piece applicable for the interval that includes − 4 . Since − 4 falls within the interval − 5 ≤ x ≤ − 2 , we substitute into the expression − x − 5 .
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Answered by ezequielburela | 2024-10-15