Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply. The domain is x. The range is y. The function is increasing over the interva…

Question

Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply. The domain is x. The range is 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 range is y ≤ 6

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

The function has a positive y-intercept

Answer 2

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=(-(-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 ≤ –2 - false.

The range is y - 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.