Question

How do you find the domain and range of `y = x^2 - 3`?

Answer 1

`x in RR, y>=-3`

Explanation:

The domain is the list of valid `x` values. Here, there are no values of `x` that are disallowed (0 is ok, small positive and negative values are ok, big positive and negative values are ok). And so we can say that the domain is:

`x in RR`

The range is the list of resulting values after we plug in `x` values. See that the smallest value `x^2` can be is 0 - it can't be negative. And so the smallest value `x^2-3` can be is `-3`. This means the range is:

`y>=-3`

Here's the graph that will show this:

graph{x^2-3}