# How do you find the domain and range for y=x^2+3?

Oct 30, 2017

Domain; $x \in \mathbb{R}$
Range; $y \ge 3$

#### Explanation:

The domain for this function can be considered by considering what values of x make y be defined, and we see evidently that $x$ can take on any real value as a simply porabola, with no asymptotes, and y would be defined; so hence $x \in \mathbb{R}$

The range can be found by considering the graph of this equation, just $y = {x}^{2}$ shifted 3 units upward;

graph{x^2+3 [-18.67, 21.33, -1.08, 18.92]}

So from this we see that $y$ has the smallest value at 3, where $x = 0$ and otherwise is $> 3$

hence $y$ is always 3 or greater.

Hence yielding a range of; $y \ge 3$