Question

Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.

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

FALSE - The domain is all real numbers
TRUE - downward parabola, max-point vertex (-2, 6) So the range is {y|y ≤ 6}.
TRUE - increases to vertex over the interval (–∞ , –2).
FALSE - The function only decreases from vertex over the interval (−2, ∞).
TRUE - The function has a positive y-intercept. -(0)^2 - 4(0) + 2 = 2