Let $g$ be the piecewise defined function shown.
$g(x)=\left\{\begin{array}{ll}
x+4, & -5 \leq x \leq-1 \\
2-x, & -1 < x \leq 5
\end{array}\right.$
Evaluate $g$ at different values in its domain.
$\begin{array}{l}
g(-4)=\square \\
g(-2)=\square \\
g(0)=\square \\
g(3)=\square \\
g(4)=\square
\end{array}$
Answer (2)
Evaluate g ( − 4 ) : Since − 5 ≤ − 4 ≤ − 1 , g ( − 4 ) = − 4 + 4 = 0 .
Evaluate g ( − 2 ) : Since − 5 ≤ − 2 ≤ − 1 , g ( − 2 ) = − 2 + 4 = 2 .
Evaluate g ( 0 ) : Since − 1 < 0 ≤ 5 , g ( 0 ) = 2 − 0 = 2 .
Evaluate g ( 3 ) : Since − 1 < 3 ≤ 5 , g ( 3 ) = 2 − 3 = − 1 .
Evaluate g ( 4 ) : Since − 1 < 4 ≤ 5 , g ( 4 ) = 2 − 4 = − 2 .
g ( − 4 ) = 0 , g ( − 2 ) = 2 , g ( 0 ) = 2 , g ( 3 ) = − 1 , g ( 4 ) = − 2
Explanation
Understanding the Piecewise Function We are given a piecewise function g ( x ) and asked to evaluate it at several points. The function is defined as:
$g(x)=\left{\begin{array}{ll} x+4, & -5 \leq x \leq-1 \ 2-x, & -1
The evaluations of the function are: g ( − 4 ) = 0 , g ( − 2 ) = 2 , g ( 0 ) = 2 , g ( 3 ) = − 1 , and g ( 4 ) = − 2 . Each value was calculated based on the segments of the piecewise function. This approach ensured that the correct equation was applied for each input value.
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