Question

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 interval (–∞ , –2).
-The function is decreasing over the interval (−4, ∞).
-The function has a positive y-intercept.

Answer 1

statements 2, 3, and 5 are true based on the graph of this function.

Answer 2

Remark
There is nothing like a graph to settle arguments about which property is to be checked.

Property One
The graph's domain is (-∞<x<∞) there are no restrictions. So property 1 is false.

Property two
The graph says that property two is true. You could complete the square to confirm it. When you do you get
y = -(x^2 + 4x) + 2
y = -(x^2 + 4x + 4) + 2 + 4
y = -(x + 2)^2 + 6 So the y value must be less that 6 ( or equal to 6)

Property Three
Property 3 is true if you are referring to the domain and neither -2 nor - infinity are included.

Property Four
Property Four is not true, It begins to decrease when x>-2 to + infinity

Property Five
It is positive (2).