Question

What is the domain and range of `y=x^2-9`?

Answer 1

Assuming we are limited to Real numbers:
Domain: `x inRR`
Range: `yin[-9,+oo)`

Explanation:

`y=x^2-9` is defined for all Real values of `x` (actually it is defined for all Complex values of `x` but let's not worry about that).

If we are restricted to Real values, then `x^2>=0`
which implies `x^2-9 >= -9`
giving `y=x^2-9` a minimum value of `(-9)` (and no limit on its maximum value.) That is it has a range from `(-9)` up to positive inifinite.