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.

For the function
f(x) = -x2 -4x + 2
The standard form is:
f(x) =-(x+2)2 + 6

Since this a quadratic function, the domain is all real numbers.
The vertex is at (-2, 6)
Since there is a negative 1 before the square term, the graph is curved downwards.
Equating the function to 0, the y-intercepts can be determined which are 0.45 and -0.45.

Therefore, from the given statements, these apply:
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.

calculista calculista · Answer 2 · 2018-08-22T16:43:44+02:00

we have

[tex] f(x) = -x^{2} - 4x + 2 [/tex]

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 [tex] (-2,6) [/tex]

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 [tex] (0,2) [/tex]

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