Question

Which statements about the graph of the function f(x) = –x2 – 4x 2 are true? check all that apply.

1.the domain is x.

2.the range is y.

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

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

5.the function has a positive y-intercept.

Answer 1

we have that

`f(x) = -x^(2) - 4x +2`

using a graph tool

see the attached figure

Statements

case a) The domain is x-------> Is False

the domain is all real numbers---------> the interval solution is (-∞,∞)

case b) The range is y ≤ 6.------> Is True

The range is the interval (-∞,6]

case c) The function is increasing over the interval (–∞ , –2).-----> Is True

See the attached figure

case d) 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 (See the attached figure)

case e) The function has a positive y-intercept.------> Is True

The value of y-intercept is
`2`

therefore

the answer is

The range is y

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

The function has a positive y-intercept

Answer 2

The statements that agree with the graph of the equation are as follows:

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

1.the domain is x.

I hope my answer has come to your help. God bless and have a nice day ahead! Feel free to ask more questions.