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

Aug 31, 2015

Domain: $\left(- \infty , + \infty\right)$
Range: $\left[0 , + \infty\right)$

#### Explanation:

The function is defined for any value of $x \in \mathbb{R}$, so its domain will have no restrictions. In interval notation, the function's domain will be $\left(- \infty , + \infty\right)$.

Since you're dealing with the square of a real number, the function can never be negative, regardless of the value of $x \in \mathbb{R}$.

${x}^{2} \ge 0 \text{, } \left(\forall\right) x \in \mathbb{R}$

This means that its range will be $\left[0 , + \infty\right)$.

graph{x^2 [-16.02, 16.02, -8.01, 8.01]}