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

The graph of the function $f(x) =-x^2-4x + 2$ is parabola with branches going down in the negative direction of y-axis. 
The vertex of parabola has coordinates:

$x_v=\dfrac{-(-4)}{2\cdot(-1)}=-2, \\ y_v=-(-2)^2-4\cdot (-2)+2=-4+8+2=6$

Then you can conclude that all x are possible, that means that the dimain is $x\in (-\infty,\infty)$ and the maximum value of y is at the vertex, then the range is $(-\infty,6]$.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.

Answer 2

Answer:

The range is {y|y ≤ 6}

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

The function has a positive y-intercept