Find the absolute minimum and absolute maximum of $|x+2|+7$

Question

Find the absolute minimum and absolute maximum of $|x+2|+7$.

$|x+2|+7$ was not stated to either be a function or not so what do I do?

Answer 1

If we define the function $f:\mathbb{R} \mapsto \mathbb{R}$ to be
$$f(x) = |x+2| + 7$$
then we can consider the expression
$$|x+2| \geq 0 \\ |x+2| + 7 \geq 7$$
and it will be obvious that this means $f$ has a global minimum of $7$.
There is no upper bound on $f$ so we can conclude that $f$ has no global maximum (as it can take values of $\infty$).