Question

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

Answer 1

This is an equation (and a function) whose graph we should know:

graph{x^2 [-20.19, 20.36, -2.03, 18.25]}

The domain is the set of all allowed `x` values. Although it is not 100% certain from the graph, it is clear from the equation, that for any number you put in for `x` you will get one and only one value for `y`. The domain is all real numbers . (The interval `(-oo, oo)`)

The range is the set of all `y` value the graph actually includes. Looking at the graph (and thinking about `x^2`, it becomes clear that `y` will never have a negative value.
It is not 100% certain from the graph, but every number that is NOT negative will be used as a `y` value. The range is `[0, oo)`