the graph of the function f(x)=(x - 3)(x + 1) is shown. which describes all of the values for which the…

Answer:

A. all real values of x where x < -1

Explanation:

Step1: Find when the function is positive

The function (f(x)=(x - 3)(x + 1)) is a quadratic function. Its roots are (x = 3) and (x=-1). The function is positive when (x<-1) or (x > 3) since ((x - 3)(x + 1)>0) in those intervals.

Step2: Determine when the function is decreasing

For a quadratic function (y = ax^{2}+bx + c) (here (y=x^{2}-2x - 3), (a = 1), (b=-2), (c=-3)), the axis of symmetry is (x=-\frac{b}{2a}=-\frac{-2}{2\times1}=1). The function is decreasing for (x<1) when (a>0).

Step3: Find the intersection

The intersection of the intervals where the function is positive ((x<-1) or (x > 3)) and decreasing ((x<1)) is (x<-1).