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.

we have

using a graph tool

see the attached figure

Statements

case 1) The domain is {x|x ≤ –2}

Is false. the domain is all real numbers---------> interval (-∞,∞)

case 2) The range is {y|y ≤ 6}.

Is true

Is a parabola open down, the vertex is the point

the range is the interval ------> (-∞,-6]

case 3) The function is increasing over the interval (–∞ , –2).

Is true (see the graph)

case 4) The function is decreasing over the interval (−4, ∞)

Is false

In the interval (-4,-2) the function is increasing and in the interval (-2, ∞) the function is decreasing

case 5) The function has a positive y-intercept

Is true

The y-intercept is the point

therefore

the answer is

The range is {y|y ≤ 6}

The function is increasing over the interval (–∞ , –2)

The function has a positive y-intercept

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed