What is the domain and range of F(x) = x^2 - 3?

Aug 11, 2015

Domain: $\left(- \infty , + \infty\right)$
Range: $\left[- 3 , + \infty\right)$

Explanation:

Your function is defined for all values of $x \in \mathbb{R}$, so its domain will have no restriction.

In order to find the function's range, you need to take into account the fact that the square of any real number is positive.

This means that the minimum value of ${x}^{2}$ is zero for $x = 0$. As a result, the minimum value of the function will be

$f \left(0\right) = {0}^{2} - 3 = - 3$

So, the domain of the function is $\mathbb{R}$, or $\left(- \infty , + \infty\right)$, and its range is $\left[- 3 , + \infty\right)$.

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