Question

The graph of the function f(x) = –(x + 6)(x + 2) is shown below.





Which statement about the function is true?


The function is increasing for all real values of x where
x < –4.

The function is increasing for all real values of x where
–6 < x < –2.

The function is decreasing for all real values of x where
x < –6 and where x > –2.

The function is decreasing for all real values of x where
x < –4.

Answer 1

expand
f(x)=-x²-8x-12
take derivitive
f'(x)=-2x-8
zero at x=-4

in x<-4, the derivitive is positive so the function is increasing
in x>-4, the derivitive is negative so the function is decreasing


increasing in (-infinity,-4)
decreasing in (-4,infinity)



first option

Answer 2

We want to see which statement is true about the function:

f(x) = -(x + 6)*(x + 2)

We will see that the correct statement is:

"The function is increasing for all real values of x where x < –4."

Which statements are correct and which aren't?

The easier way to check this is by using the graph of the function, which you can see below.

There you can see that:

• The graph increases for all values of x < -4
• The graph decreases for all values of  x > -4.

From that, then we can see that the only correct statement is:

"The function is increasing for all real values of x where x < –4."

If you want to learn more about quadratic functions, you can read:

https://brainly.com/question/1214333