Question

In a paragraph, explain what the domain and range is for the function f(x) = x2 + 4x - 21.

Answer 1

Domain: Anything at all. All numbers and sub-divisions of a number line. - ∞ < x < ∞

The range is much harder. You could complete the square to get the range, which I will do after we get the answer. The simplest way to get the smallest part of the range is to graph the quadratic. The lowest point is at (-2, -25) so the range is

Range: -25 ≤ y < ∞

Completing the square.

y = x^2 + 4x - 21

y = (x^2 + 4x) - 21

y = (x^2 + 4x + (4/2)^2 ) - 21 - (4/2)^2

y = (x^2 + 4x + 4) - 21 - 4

y = (x + 2)^2 - 25

The minimum point is (- 2,-25) just as the graph predicted.