Question

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

Answer 1

`x in RR`

Explanation:

`x^2-2` is a polynomial, which is defined for all real numbers.

This isn't something mysterious and earth-moving about polynomials, but any number, we can square it, and take it to whatever power for that matter and get a result. And we can subtract `2` from everything. Thus

`x inRR`

Hope this helps!

Answer 2

Domain: `{x|x " is " RR}` or `(-oo, oo)` in interval notation.

Range: `{y|y >=-2)` or `[-2, oo)`

Explanation:

This function is a quadratic `ax^2+bx+c` and all quadratics are parabolas their domain is not restricted and is all real numbers:

Domain: `{x|x " is " RR}` or `(-oo, oo)` in interval notation.

The range is more interesting as it is shifted down 2 from the parent function:

Range: `{y|y >=-2)` or `[-2, oo)`

graph{x^2 -2 [-10, 10, -5, 5]}