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Thread: The intervals where the function is positive and negative.

  1. #1
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    The intervals where the function is positive and negative.

    Having trouble with finding the "the intervals where the function is positive and negative", I know what the zeros are but I'm not sure how to word it correctly. Heres a picture of the question and my answers to them.

    The intervals where the function is positive and negative.-0adgyhl.pngThe intervals where the function is positive and negative.-screen-shot-2017-11-13-2.43.35-pm.png
    Example in my notes.The intervals where the function is positive and negative.-givnjri.png

    I feel like I'm either messing up my > or < signs or my zeros are wrong.
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  2. #2
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    Re: The intervals where the function is positive and negative.

    Let's start with a). If $x<-2$, then we have $f(x)$ is the product of 4 negative numbers: $-4, (x-3), (x+2), (2x-1)$, so it is positive.
    If $-2<x<\dfrac{1}{2}$, we have $f(x)$ is the product of three negative numbers: $-4, (x-3), (2x-1)$ and one positive number $(x+2)$, so it is negative.
    If $\dfrac{1}{2} < x < 3$, we have $f(x)$ is the product of two negative numbers: $-4, (x-3)$ and two positive numbers: $(x+2), (2x-1)$, so it is positive.
    If $3 < x$, we have $f(x)$ is the product of one negative number: $-4$ and there positive numbers: $(x+2), (2x-1), (x-3)$.

    For part (b), you have the zeros wrong. -2 is not a zero, but 0 is.
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  3. #3
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    Re: The intervals where the function is positive and negative.

    What does "zero of a function" mean?

    In the functions you are asked about, what are they?

    With respect to all values less than but close enough to the zero, a continuous function function can ONLY be everywhere positive, everywhere negative, or everywhere zero. With respect to values greater then but close enough to the zero, a continuous function can ONLY be everywhere positive, everywhere negative, or everywhere zero. How do you determine which of those possibilities applies? Once you make those determinations, how does that help you answer the question?
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