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

Jun 1, 2018

$x \in \mathbb{R}$

#### 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

$x \in \mathbb{R}$

Hope this helps!

Jun 1, 2018

Domain: $\left\{x | x \text{ is } \mathbb{R}\right\}$ or $\left(- \infty , \infty\right)$ in interval notation.

Range: $\left\{y | y \ge - 2\right)$ or $\left[- 2 , \infty\right)$

#### Explanation:

This function is a quadratic $a {x}^{2} + b x + c$ and all quadratics are parabolas their domain is not restricted and is all real numbers:

Domain: $\left\{x | x \text{ is } \mathbb{R}\right\}$ or $\left(- \infty , \infty\right)$ in interval notation.

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

Range: $\left\{y | y \ge - 2\right)$ or $\left[- 2 , \infty\right)$

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