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

1 Answer
VNVDVI
Mar 26, 2018

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]

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