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The graph of which function is decreasing over the interval (–4, ∞)?

f(x) = (x + 4)2 + 4
f(x) = –(x + 4)2 + 4
f(x) = (x – 4)2 – 4
f(x) = –(x – 4)2 – 4

Respuesta :

apologiabiology
ok, logic
all of them are parabolas

1st and 3rd are opening up, so they defenitely increase, so no

decraseing
the vertex hs to be be at x=-4
y=a(x-h)^2+k
h has to be -4
y=a(x+4)^2+k
the answer is 2nd one or f(x)=-(x+4)^2+4
azikennamdi

The function whose graph is decreasing over the interval of (-4, ∞) is:
"F(x) = - (x+4) (2+4) - Option B. This solution is arrived at using the logic of Graph of Functions.

What is the Proof that Option B is the function whose graph is decreasing over the Interval (-4, ∞)

If we expand the function - (x+4)[tex]^{2+4}[/tex] what that gives us is:

(- X- 4)[tex]^{6}[/tex] which is tending toward <0

According to the rules of Increasing or decreasing functions, if the derivative of a function say F'(X) > 0 (that is tending towards greater than zero), the function is INcreasing.

If however, F'(X) < 0, at each point of the interval I, then the function is said to be decreasing over the interval I

Hence the correct answer is B: f(x) = –(x + 4)2 + 4

Learn more about Graphs of Functions at:
https://brainly.com/question/3144397

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