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

May 29, 2017

Find all possible values. In this case, there are no limits, thus, $\text{D} : \left\{x \in \mathbb{R}\right\}$.

#### Explanation:

A parabola will always have a domain of $\left\{x \in \mathbb{R}\right\}$. This is because, if you look at a graph, there are no limits to the domain, unless provided context that restricts the domain.

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

As you can see, no matter how much you zoom out, there will always be an $x$-value.

EXTRA

The range however, will have a limit to the parabola function.

This is all dependent on the $c$-value.

If we get the parent function, $f \left(x\right) = {x}^{2}$, and graph it.

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

We can see that the only possible $y$-values are values above $y = 0$. Thus, the range is $\text{R} : \left\{y \in \mathbb{R} | 0 \le y\right\}$.

Hope this helps :)