Question

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

Answer 1

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|x ≤ –2}. 

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Answer 2

we have that

$f(x) = -x^{2} - 4x +2$

using a graph tool

see the attached figure

Statements

case a) The domain is {x|x ≤ –2}-------> Is False

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

case b) The range is {y|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|y ≤ 6}

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

The function has a positive y-intercept