Question

How do you find the domain and range of `y = sqrt(9 + x)`?

Answer 1

Domain: `[-9,oo)`
Range: `[0,oo)`

Explanation:

Assuming we are working strictly within the reals, the square root function requires nonnegative values. Thus the domain of the function `f(x) = sqrt(9+x)` is the set of values for `x` such that `9+x>=0`, that is, where `x>=-9`.

As `9+x` varies from `0` to `oo`, `sqrt(x+9)` varies from `0` to `oo`.

Thus, the domain of `sqrt(x+9)` is `[-9,oo)` and its range is `[0,oo)`