Question

he graph of the function f(x) = (x +2)(x + 6) is shown below.

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).

What is true about the domain and range of the function?

The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.

Answer 1

The first choice.

f(x) = (x+2)(x+6) is a polynomial so its domain is all real numbers. The parabola opens upward and has vertex at (−4, −4), so the minimum y-value is −4 and the range is y ≥ −4.