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? 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

A: on edge.

Explanation:

Answer 2

1. The ''x-intercepts" of the graph of f(x) are those x-es such that

(x+2)(x+6)=0, so the x-intercepts or the roots are -2 and -6.

2. The axis of symmetry is the vertical line through the midpoint of -2 and -6, that is -4.

3. The vertex is the point (-4, f(-4))=(-4,(-4+2)(-4+6) )=(-4, (-2)(2))=(-4, -4)

4. The standard form of (x+2)(x+6) is
`x^(2) +8x+12`. The coefficient of
`x^(2)` is possitive so the parabola opens upwards.

5. This means the vertex (-4, -4) is the lowest point, so f(x) takes all values from -4 (inclusive) to + infinity. This determines the range

6. Any x can be "plugged in" f(x)=(x+2)(x+6) and be calculated, so x can be any number in R. This determines the domain to be all R.

7. Right choice is "The domain is all real numbers, and the range is all real numbers greater than or equal to –4."