Answer:
Step-by-step explanation:
f(x) = (x + 2)(x +6)
1) The function is positive for all real values of x where x > –4 :
COUNTER-EXAMPLE : x = - 3 you have -3>-4 but (-3+2)(-3+6) = -1 ×3 =-3 no positive .
2) The function is positive for all real values of x where
x < –6 or x > –3.
COUNTER-EXAMPLE : x = - 2.5 you have -2.5>-3 but (-2.5+2)(-2.5+6) = -0.5 ×3.5 =-1.75 no positive .
same method for the statement : "The function is negative for all real values of x where
x < –2."
conclusion : statement about the function is true: "The function is negative for all real values of x where
–6 < x < –2."
.
Answer:
The function is negative for all real values of x where
–6 < x < –2
Step-by-step explanation:
the function f(x) = (x + 2)(x + 6)
LEts find the x intercept of the given function
0 = (x+2)(x+6)
x+2=0 so x=-2
x+6 = , so x=-6
x intercepts are -6 and -2
Lets draw a number line and use x intercepts and make 3 intervals
- infinity to -6 , -6 to -2 and -2 to infinity
LEts pick a number from each interval and check with f(x)
x<-6, pick -7
f(x) = (x + 2)(x + 6)
f(-7)=(-7 + 2)(-7 + 6) =5 , which is positive
–6 < x < –2, pick 4
f(-4)=(-4 + 2)(-4 + 6) =-4 , which is negative
x>-2, pick 0
f(0)=(-0+ 2)(0 + 6) =12 , which is positive
The function is negative for all real values of x where
–6 < x < –2
