Question

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

Answer 1

`[-1, oo]`

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 `[-1,oo]` as `-1` is the lowest point on the graph along the `y`-axis and `oo` 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]}