Question

What the domain and range is for the function f(x) = x2 + 4x - 21.

Answer 1

Explanation:

Please use " ^ " to denote exponentiation: f(x) = x^2 + 4x - 21.

This function has a graph which is a parabola that opens up.

Its vertex is found by completing the square:

x² + 4x + 4 - 4 - 21, or

(x + 2)² - 25

Comparing this to the standard equation

(x - h)² + k, we see that h = -2 and k = -25.

Thus, the vertex (and the minimum of this function) is (-2, -25).

Thus, the range is [-25, ∞ ). This being a polynomial function, it has no restrictions on the domain: the domain is (-∞, ∞ )