# What is the range of the function y=x^2-1?

May 29, 2018

$\left[- 1 , \infty\right]$

#### Explanation:

For this function, you can see that the basic function is ${x}^{2}$. In this case, the ${x}^{2}$ graph has been shifted down the $y$-axis by $1$.

In knowing this information the range can be observed as $\left[- 1 , \infty\right]$ as $- 1$ is the lowest point on the graph along the $y$-axis and $\infty$ as the graph is observed to continue (has no restrictions).

The easiest way to find the range is to draw the graph.

graph{x^2-1 [-2.5, 2.5, -1.25, 1.25]}