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1 March, 20:53

The graph of the function f (x) = (x - 3) (x + 1) is shown.

Which describes all of the values for which the graph is

positive and decreasing?

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Answers (1)
  1. 1 March, 23:46
    0
    Step-by-step explanation:

    Option A. All the real values of x where x < - 1

    Procedure

    Solve the inequality:

    (x - 3) (x+1) >0

    That happens in two cases.

    1) When both factors >0

    x-3>0 and x+1>0

    x>3 and x >-1

    The intersection is x >3

    2) When both factors <0

    x-3<0 and x+1<0

    x<3 and x<-1

    the intersection is x<-1.

    We have obtained that the function is positive for the intervals x 3. But in one of those intervals the function is decresing and in the other is increasing.

    You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.
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