# How do you find the domain and range of f(x) = x^2+3?

Jun 22, 2018

$x \in \mathbb{R} , y \in \left[3 , \infty\right)$

#### Explanation:

$f \left(x\right) = {x}^{2} + 3 \text{ is defined for all real values of x}$

$\text{domain is } x \in \mathbb{R}$

$\left(- \infty , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

$\text{the vertex of "x^2+3" is } \left(0 , 3\right)$

$\text{since "a>0" it is a minimum turning point } \bigcup$

$\text{range is } \left[3 , \infty\right)$
graph{x^2+3 [-10, 10, -5, 5]}