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`