Question

GRAPHS EQUATIONS Domain: y = x2-1 Range: Domain: Range: Function? Function?

Answer 1

The expressi

`y=x^2-1`

and we would like to know the domain and range of the function. Since for every x value we give to the equation the result will always be a real number the domain of this function is

`\text{dom y=(-}\infty,\infty)`

Now to find the range of the function we solve the equation for x.

`\begin{gathered} y=x^2-1 \\ x^2=y+1 \\ x=\pm\sqrt[]{y+1} \end{gathered}`

This root will only exist if

`\begin{gathered} y+1\ge0 \\ y\ge-1 \end{gathered}`

Therefore the range of the function is:

`\text{range y=}\lbrack-1,\infty)`