Question

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

A.f(x) = (x + 4)2 + 4
B.f(x) = –(x + 4)2 + 4
C.f(x) = (x – 4)2 – 4
D.f(x) = –(x – 4)2 – 4

Answer 1

I think second must b the answee

Answer 2

This can be solved by the method of elimination.

We have been given that the function should decrease over (-4,∞)

So, since its between -4 and ∞ , we can eliminate option A and C. This is because options A and C are actually increasing over (-4,∞) and not decreasing.

So, this leaves us with options B and D. Next we find the vertex of the two functions. The vertex of Option B, that is
`-(x+4)^2 +4` lies at the point (-4,4) and decreases with x over the interval (-4,∞).

Whereas the option D,
`-(x-4)^2+4` has the vertex at (4,4) and hence the interval is not between -4 and infinite.

Hence Option B,
`-(x+4)^2 +4` is the answer asthe function is decreasing over the interval (–4, ∞)