Question

What is the domain and range of `f(x)= x^2 - 2x -3`?

Answer 1

Domain: `x in RR`
Range: `f(x) in [-4,+oo)`

Explanation:

`f(x)=x^2-2x-3` is defined for all Real values of `x`
therefore the Domain of `f(x)` covers all Real values (i.e. `x in RR`)

`x^2-2x-3` can be written in vertex form as `(x-color(red)1)^2+color(blue)((-4))` with vertex at `(color(red)1,color(blue)(-4))`
Since the (implied) coefficient of `x^2` (namely `1`) is positive, the vertex is a minimum
and `color(blue)((-4))` is a minimum value for `f(x)`;
`f(x)` increases without bound (i.e. approaches `color(magenta)(+oo)`) as `xrarr +-oo`
so `f(x)` has a Range of `[color(blue)(-4),color(magenta)(+oo))`