# What is the range of f(x)=|x+4|+2?

Begin by finding out the range of $g \left(x\right) = | x + 4 |$, or for that matter, $g \left(x\right) = | x |$. The range is obviously given by $\left[0 , \setminus \infty\right)$ for both of them.
Now, what is the range of $f \left(x\right) = | x + 4 | + 2$? It can be seen that the difference between $| x + 4 | + 2$ and $| x + 4 |$ is $2$. Literally.
If you add $2$ to $g \left(x\right)$, you get $f \left(x\right)$. This means that you're shifting the whole range of $g \left(x\right)$ by $2$.
Therefore, the range of $f \left(x\right)$ is $\left[2 , \setminus \infty\right)$ because that is what you get when you shift the range of $g \left(x\right)$, $\left[0 , \setminus \infty\right)$, by $2$.