Question

How do I find the range of these functions without using a graph `y=-2+sqrt(16-x^2)`?

Answer 1

`-2<=-2+sqrt(16-x^2)<=2`

Explanation:

Since `sqrt(16-x^2)>=0` we get
`-2<=-2+sqrt(16-x^2)`
Since `-x^2<=0` we get

`sqrt(16-x^2)<=4`
or
`-2+sqrt(16-x^2)<=2`