Find the maximum and minimum values of the function
$
f(x) = |x + 2| - 1
$

Q: Find the maximum and minimum values of the function $ f(x) = |x + 2| - 1 $

Explanation: Since $|x + 2| \geq 0$ for all $x \in \mathbb{R}$, \[ f(x) = |x + 2| - 1 \geq -1 \] Equality occurs when $|x + 2| = 0 \Rightarrow x = -2$. \[ \text{Minimum value of } f = f(-2) = | -2 + 2 | - 1 = -1 \] There is no maximum value since $|x + 2|$ grows unbounded as $x \to \infty$.

Question

Find the maximum and minimum values of the function  
$
f(x) = |x + 2| - 1
$

Accepted Answer

Explanation: Since $|x + 2| \geq 0$ for all $x \in \mathbb{R}$,  
$$
f(x) = |x + 2| - 1 \geq -1
$$  
Equality occurs when $|x + 2| = 0 \Rightarrow x = -2$.  
$$
\text{Minimum value of } f = f(-2) = | -2 + 2 | - 1 = -1
$$  
There is no maximum value since $|x + 2|$ grows unbounded as $x \to \infty$.

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