Question

Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Select three options.

The domain is {x|x ≤ –2}.
The range is {y|y ≤ 6}.
The function is increasing over the interval (–∞ , –2).
The function is decreasing over the interval (−4, ∞).
The function has a positive y-intercept.

Answer 1

The true statements are:

- The range is {y | y ≤ 6}. (Vertex form: f(x) = −(x+2)^2 + 6, so maximum y = 6.)
- The function is increasing over the interval (−∞, −2). (Left of the vertex at x = −2 it rises.)
- The function has a positive y-intercept. (f(0) = 2 > 0.)

The other two statements are false: the domain is all real numbers, and the function is not decreasing on (−4, ∞) (it increases on (−4, −2) and decreases for x > −2).