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 ≤ –2.
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 domain of the function is all range real number. The range is all real numbers less than or equal to 6. The function is a parabola curving downwards, so the function is increasing over the interval (–∞ , –2) and the function is decreasing over the interval (−4, ∞). When x = 0, the function has both positive and negative y-intercepts.

Answer 2

we have

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

using a graph tool

see the attached figure

statements

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

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

b) The range is y ≤ 6.------> Is True

The range is the interval (-∞,6]

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

See the attached figure

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`