Question

How do you find the domain and range for `y =sqrt(9-x^2)`?

Answer 1

Domain: `x in [-3,+3]`
Range: `yin [0,3]`

Explanation:

I assume that we are dealing only with Real numbers.

For Real numbers `sqrt(a)` is only defined if `a>=0`
`rarr (9-x^2)>=0`
`rarr abs(x)<=3`
which gives us the Domain.

The maximum value of `sqrt(9-x^2)` occurs when `x=0` and
this maximum is `sqrt(9) = 3`
The minimum value of `sqrt(9-x^2)` occurs when `x=+-3` and
this minimum is `sqrt(9-9) =0`
which together give us the Range.