# How do you find the domain and range of f(x)=x^2+5?

Jul 3, 2018

The domain is $x \in \mathbb{R}$. The range is $y \in \left[5 , + \infty\right)$

#### Explanation:

The function is

$y = {x}^{2} + 5$

This is a polynomial function, $x$ can take any value.

Therefore, the domain is $x \in \mathbb{R}$

The minimum value of $y$ is when $x = 0$

$\implies$, $y = 5$

And due to the presence of ${x}^{2}$, $y$ can take only positive values as

${\left(- x\right)}^{2} = {x}^{2}$

Therefore, the range is $y \in \left[5 , + \infty\right)$

graph{x^2+5 [-56.73, 60.37, -20.6, 37.95]}