# What is the domain and range of y=x^2+4?

Sep 1, 2017

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$.
Range: $y \ge 4 \mathmr{and} \left[4 , \infty\right)$

#### Explanation:

$y = {x}^{2} + 4$ . Domain : Any real value of $x$ i.e

$x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$

Range: This is a parabola equation of which vertex form is

 y= a(x-h)^2+k or y= 1(x-0)^2+4; (h.k) being vertex.

Here vertex is at (0,4) ; a >0  . Since $a > 0$ , the parabola opens

upward . The vertex $\left(0 , 4\right)$ is the lowest point of the parabola.

So Range is $y \ge 4 \mathmr{and} \left[4 , \infty\right)$

graph{x^2+4 [-20, 20, -10, 10]} [Ans]