Question

The graph of the function f(x) = (x +2)(x + 6) is shown below. What is true about the domain and range of the function?

Answer 1

The graph of the function:

$f(x)=(x+2)(x+6)$

is indicated in the Figure bellow. This graph represents a quadratic function, that is, a parabola. The following is true about the domain and range:

1. Domain

The domain is the set of all real numbers. In fact, this is true for all the quadratic functions. There is no any restriction in the domain. This can be written in a mathematical language as follows:

$\boxed{-\infty$

2. Range

The range of this function is all the real number greater or equal to -4 as indicated in the Figure, this is found by the inverse function:

$\boxed{y\geq -4}$

Answer 2

A. The domain is all real numbers, and the range is all real numbers greater than or equal to -4.