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Given: $f(x)=|x+2|$

Now,

$|x+2| \geq 0$ for all $x \in \mathrm{R}$

Thus, $f(x) \geq 0$ for all $x \in \mathbf{R}$

Therefore, the minimum value of $f$ at $x=-2$ is 0 .

Since $f(x)$ can be enlarged, the maximum value does not exist, which is evident in the graph also. Hence, the function $f$ does not have a maximum value.