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

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

Explanation:

Step1: Analyze the function (f(x)=-(x + 3)(x - 1))

The roots of the quadratic function (y =-(x + 3)(x - 1)) are (x=-3) and (x = 1). Since the coefficient of (x^{2}) is (-1<0), the parabola opens downwards.

Step2: Determine where the function is positive or negative

The function (y=f(x)) is positive (above the (x)-axis) when (-3<x<1) and negative (below the (x)-axis) when (x<-3) or (x > 1).

Answer:

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