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Thread: Increasing & Decreasing of a function

  1. #1
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    Increasing & Decreasing of a function

    Here's a quite simple question. But well, I've dropped outta school for about 3.5 years, now that I got back to school, I'd require to learn some basics before heading to advanced stuffs.

    I'm kinda confused on the increasing and decreasing of a function when the function has an absolute value( |a| )

    Eg. f(x)=| x-2 |

    how do I differentiate them? Or what shall I do?

    Thank you.

    Tim
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  2. #2
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    Quote Originally Posted by techdx69 View Post
    I'm kinda confused on the increasing and decreasing of a function when the function has an absolute value( |a| )
    Eg. f(x)=| x-2 |how do I differentiate them? Or what shall I do?
    Just plot the function. See where it is decreasing or increasing.
    Do several of them to see a general pattern.
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  3. #3
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    Sorry but unfortunately as I've mentioned its been a while since I've studied math and back then I do not acquired enough basics in math. And even if I do, I'd not remember any of em by now. And I do not remember how to sketch a graph. So if you don't mind, please teach me how to or give me a tutorial video with it. And its the "| |" absolute , thats bothering me in this question. :S
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  4. #4
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    First, you can plot the graph of something like f(x) = |x - 2| by computing the value of f in several points, such as x = 0, 1, 2, 3, 4 and then connecting the dots.

    Also, $\displaystyle |x|=
    \begin{cases}
    x, & x\ge 0\\
    -x, & x < 0
    \end{cases}$. So, $\displaystyle |x - 2|=
    \begin{cases}
    x - 2, & x - 2\ge 0\\
    -(x - 2), & x - 2 < 0
    \end{cases}$. Further, $\displaystyle x - 2\ge 0$ iff $\displaystyle x\ge 2$ and $\displaystyle x - 2 < 0$ iff $\displaystyle x < 2$. So, $\displaystyle |x - 2|=
    \begin{cases}
    x - 2, & x\ge 2\\
    -(x - 2), & x < 2
    \end{cases}$. Therefore, for $\displaystyle x\ge 2$ you can draw the graph of x - 2. For x < 2, you need the graph of -(x - 2) = 2 - x. It can either be drawn directly, or you can use the fact that for any function g(x), the graph of -g(x) is obtained from the graph of g(x) by reflecting it with respect to the x-axis.
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