Question

What is the domain and range of y=x^2-2?

Thank you♡

Answer 1

`x inRR,y in[-2,oo)`

Explanation:

`"y is defined for all real values of x"`

`"domain is "x inRR`

`(-oo,oo)larrcolor(blue)"in interval notation"`

`"the quadratic in the form "y=x^2+c`

`"has a minimum turning point at "(0,c)`

`y=x^2-2" is in this form with "c=-2`

`"range is "y in[-2,oo)`
graph{x^2-2 [-10, 10, -5, 5]}

Answer 2

Since there no are fractions, roots, etc. involved the domain of `x` is not limited. `- oo < x< +oo`

Explanation:

The range of `y`:
`x^2` is always non-negative:
`x^2>=0->x^2-2>= -2`

So: `-2<=y<+oo`