Your post would be clearer if you'd please put each function on its own line:
f(x) = (x + 4)2 + 4
f(x) = –(x + 4)2 + 4
f(x) = (x – 4)2 – 4
f(x) = –(x – 4)2 – 4
Also, use "^2" to denote "squaring." x2 has no meaning.
f(x) = (x + 4)^2 + 4 has a parabolic graph with vertex (-4,4). It increases steadily once x is greater than -4. Reject this choice.
f(x) = –(x + 4)^2 + 4 has a parab. graph with vertex (-4,4) also. It decreases steadily once x is greaster than -4. This is the answer.
Analyze the other 2 possible answers in the same way, please.
Answer:
Option B.
Step-by-step explanation:
We have to find the function which is decreasing over the interval of (-4, ∞).
Option A. f(x) = (x + 4)²+ 4
This graph is opening upwards and having vertex at ( -4, 4).
In the interval (-4, ∞) the given function will increase.
Therefore, incorrect option.
Option B. f(x) = -(x + 4)² + 4
Parabola represented by this function is opening downwards has the vertex as ( -4, 4)
Function f(x) will decrease between the given interval.
Therefore, this option is correct.
Option C.f(x) = (x - 4)² - 4
This parabola is opening upwards and having vertex at ( 4, -4)
Function will increase in the given interval.
Therefore, f(x) is not correct.
Option D. f(x) = -(x - 2)²- 4
Given parabola is opening downwards and vertex of the function is (2, -4)
This parabola is increasing between this interval.
Therefore, this option is incorrect.
