Question

How do you find the domain and the range of the function `f(x)= x^2 - 2x -3`?

Answer 1

Domain: `(-oo, oo)` Range: `[-4, oo)`

Explanation:

In general, the domain, or `x` values which yield an output `f(x),` of a polynomial function is all real numbers, denoted by `(-oo, oo)` in interval notation.

Range becomes more specific. This is a quadratic function. In general, the range, or `y-`values for which the function exists, of a quadratic with vertex at `(h,k)` is `[k, oo)`, OR `(-oo, k]` if the parabola is inverted (it isn't in this case -- we don't begin with `-x^2`).

So, let's find the vertex.

We have `f(x)=ax^2+bx+c=x^2-2x-3, a=1, b=-2, c=-3`

`h=-b/(2a)=2/2=1`

`k=f(h)=f(1)=1-2-3=-4`

The range is then `[-4, oo]`