the graph of the function f(x)=-(x + 3)(x - 1) is shown below. which statement about the function is true…

the graph of the function f(x)=-(x + 3)(x - 1) is shown below. which statement about the function is true? the function is positive for all real values of x where x < -1. the function is negative for all real values of x where x < -3 and where x > 1. the function is positive for all real values of x where x > 0. the function is negative for all real values of x where x < -3 or x > -1.

the graph of the function f(x)=-(x + 3)(x - 1) is shown below. which statement about the function is true? the function is positive for all real values of x where x < -1. the function is negative for all real values of x where x < -3 and where x > 1. the function is positive for all real values of x where x > 0. the function is negative for all real values of x where x < -3 or x > -1.

Answer

Answer:

The function is negative for all real values of (x) where (x < - 3) and where (x>1).

Explanation:

Step1: Find the roots of the function

Set (f(x)=-(x + 3)(x - 1)=0). Then (x=-3) or (x = 1) are the roots.

Step2: Analyze the sign of the quadratic function

The quadratic function (y=-(x + 3)(x - 1)=-x^{2}-2x + 3) has a negative leading - coefficient ((a=-1<0)), so the parabola opens downwards.

Step3: Determine the intervals of sign

For (x<-3), let (x=-4), then (f(-4)=-(-4 + 3)(-4 - 1)=-(-1)\times(-5)=-5<0). For (-3<x<1), let (x = 0), then (f(0)=-(0 + 3)(0 - 1)=3>0). For (x>1), let (x = 2), then (f(2)=-(2 + 3)(2 - 1)=-5<0). So the function is negative for (x<-3) and (x > 1).