Question

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

Answer 1

Begin by finding out the range of `g(x) = |x+4|`, or for that matter, `g(x) = |x|`. The range is obviously given by `[0,\infty)` for both of them.

Now, what is the range of `f(x) = |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(x)`, you get `f(x)`. This means that you're shifting the whole range of `g(x)` by `2`.

Therefore, the range of `f(x)` is `[2,\infty)` because that is what you get when you shift the range of `g(x)`, `[0,\infty)`, by `2`.