Question

question
$f(x)=\

$$\begin{cases}5 & \\text{for } -4 < x < 0 \\\\ -2 & \\text{for } x = 0 \\\\ \\frac{1}{3}x + 5 & \\text{for } 0 < x \\leq 3\\end{cases}$$

$
find $f(-4)$
answer attempt 1 out of 2

Explanation:

Step1: Check domain of $f(-4)$

The piecewise function has three domains: $-4 < x < 0$, $x=0$, and $0 < x \leq 3$. The input $x=-4$ does not fall into any of these defined intervals.

Step2: Determine function value

Since $x=-4$ is not included in any of the function's specified domains, $f(-4)$ is not defined for this piecewise function.

Answer:

$f(-4)$ is not defined (the input $x=-4$ is not in the domain of the function)