Question

The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true? The function is positive for all real values of x where x > –4. The function is negative for all real values of x where –6 < x < –2. The function is positive for all real values of x where x < –6 or x > –3. The function is negative for all real values of x where x < –2.

Answer 1

he function is negative for all real values of x where –6 < x < –2 (True)

Explanation:

(x+2) can be written as

x + 2 = 0

x = -2

(x+6) can be written as

x + 6 = 0

x = -6

Both of these can be written as -6 < x < -2

1) he function is positive for all real values of x where x > –4.

(All values are between -2 and -6 and they are negative therefore this statement is false.)

2) True (explained above)

3) The function is positive for all real values of x where x < –6 or x > –3.

(x>-2 includes -3 but x>-3 does not include -3 therefore, this is false.)

4) The function is negative for all real values of x where x < –2. (It is not negative for all values as there is a limit between -2 and -6.)

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