Question

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

Answer 1

The function

\displaystyle f\left(x\right)={x}^{3}-12x

f(x)=x

3

−12x is increasing on

\displaystyle \left(-\infty \text{,}-\text{2}\right){{\cup }^{\text{ }}}^{\text{ }}\left(2,\infty \right)

(−∞,−2)∪

 

 

(2,∞) and is decreasing on

\displaystyle \left(-2\text{,}2\right)

(−2,2).

Answer 2

Answer:

Option B - $f(x)=-(x+4)^2+4$    

Step-by-step explanation:

Given : Function is decreasing over the interval (-4,∞).

To find : Which function is decreasing over the interval (-4,∞)

The function is of the form,  $f(x)=a(x-h)^2+k$

where (h,k) is the vertex.

Option second is the correct option

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

where a=-1 , h=-4 and k=4

Vertex =(-4,4)

This is a maximum graph because a= -1<0

Since it is a maximum graph,the function increases on the interval (-∞,-4)  and decreases on the interval (-4,∞).

Refer the attached graph.

Therefore, option B is correct.