Find the maximum and minimum values of the function
$
g(x) = -|x + 1| + 3
$

Q: Find the maximum and minimum values of the function $ g(x) = -|x + 1| + 3 $

Explanation: Since $-|x + 1| \leq 0$, \[ g(x) = -|x + 1| + 3 \leq 3 \] Equality occurs when $|x + 1| = 0 \Rightarrow x = -1$. \[ \text{Maximum value of } g = g(-1) = -| -1 + 1 | + 3 = 3 \] There is no minimum value since $-|x + 1|$ decreases without bound.

Question

Find the maximum and minimum values of the function  
$
g(x) = -|x + 1| + 3
$

Accepted Answer

Explanation: Since $-|x + 1| \leq 0$,  
$$
g(x) = -|x + 1| + 3 \leq 3
$$  
Equality occurs when $|x + 1| = 0 \Rightarrow x = -1$.  
$$
\text{Maximum value of } g = g(-1) = -| -1 + 1 | + 3 = 3
$$  
There is no minimum value since $-|x + 1|$ decreases without bound.

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