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.

The graph of the function is parabola with branches going down in the negative direction of y-axis. 
The vertex of parabola has coordinates:



Then you can conclude that all x are possible, that means that the dimain is and the maximum value of y is at the vertex, then the range is .The function is increasing for x<-2 and decreasing for x>-2 (since vertex is the maximum point).
When x=0, y=2. 
Hence,
The domain is {x|x ≤ –2} - false.

The range is {y|y ≤ 6} - true.

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

The function is decreasing over the interval (−4, ∞) - false.

The function has a positive y-intercept - true.

With a continuous thought process.