Question

How do you find the domain and range of `f(x)=x^2-1`?

Answer 1

`x inRR`
`y in[-1,oo)`

Explanation:

`"This is a polynomial of degree 2 and is well defined for"`
`"all real values of x"`

`"domain is "x inRR`

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

`"to find the range we require the vertex and whether it"`
`"is a maximum or minimum"`

`"the vertex of a parabola in the form "y=ax^2+c`

`"is "(0,c)`

`color(magenta)" vertex "=(0,-1)`

`"since "a>0" then minimum turning point " uuu`

`"range is "y in[-1,oo)`
graph{x^2-1 [-10, 10, -5, 5]}