# What are the domain and range of Y=3x^2 ?

Nov 5, 2017

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

#### Explanation:

$Y = 3 {x}^{2}$

$Y$ is defined $\forall x \in \mathbb{R} \to$ Domain of $Y$ is $\left(- \infty , + \infty\right)$

${x}^{2} \ge 0 \forall x \in \mathbb{R}$

$\therefore Y \ge 0 \forall x \in \mathbb{R}$

Hence the Range of $Y$ is $\left[0 , + \infty\right)$

We can conclude the domain and range for the graph of $Y$ below.

graph{3x^2 [-10, 10, -5, 5]}