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

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 2

Option B.

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.