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Math Help - Piecewise defined functions and integrals

  1. #1
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    Piecewise defined functions and integrals

    I'm not even sure where to begin on this one, or how f(x) and g(x) are related...

    Let
    ------{0 if x< 0
    ------{x if 0 \leq x \leq 1
    f(x) = {2-x if 1 < x \leq 2
    ------{0 if x> 2

    (excuse the mess, but I've no idea how to do the piecewise functions with math tags.)

    a) Find an expression for g(x) similar to the one for f(x), i.e., a piecewise defined function.

    b)sketch the graphs of f(x) and g(x) on the same coordinate system.
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  2. #2
    GAMMA Mathematics
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    g(x) is one function that looks like f(x)... it starts at (0,0) and goes to (1,1) and then down to (2,0) and stops. This is the nature of absolute value of a function, notably:

    g(x)=-|x-1|+1 for the domain of x: (0,2)

    HINT: start with g(x) = |x| and then flip it, shift it horizontally, and then vertically
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  3. #3
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    I'm a little confused about the first part, how I know that g(x) is an absolute value function?
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    GAMMA Mathematics
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    Quote Originally Posted by ebonyscythe View Post
    I'm a little confused about the first part, how I know that g(x) is an absolute value function?
    Because of the shape of f(x), it basically looks like the karat symbol that is above your six on the keyboard.
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  5. #5
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    Well I understand that, it's just I'm not sure how the two functions are connected. How can I conclude that g(x) is an absolute value from f(x)? Is it because g(x) is the integral of f(x)?
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    Forum Admin topsquark's Avatar
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    I'm beginning to believe in psychic communication...

    Where, in the original post or anywhere else, is g(x) defined??

    -Dan
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    Quote Originally Posted by ebonyscythe View Post
    I'm not even sure where to begin on this one, or how f(x) and g(x) are related...

    Let
    ------{0 if x< 0
    ------{x if 0 \leq x \leq 1
    f(x) = {2-x if 1 < x \leq 2
    ------{0 if x> 2

    (excuse the mess, but I've no idea how to do the piecewise functions with math tags.)

    a) Find an expression for g(x) similar to the one for f(x), i.e., a piecewise defined function.

    b)sketch the graphs of f(x) and g(x) on the same coordinate system.
    What do you know about g(x), I see no information on how it is related to
    f(x) in your post.

    RonL
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  8. #8
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    Whoops, I did cut off the question... sorry about that.

    g(x) = \int_0^x f(t)dt

    That's probably pretty important, yeesh.
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  9. #9
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    Anyone? I gotta leave for Psych soon, so I won't be around much longer.
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ebonyscythe View Post
    Anyone? I gotta leave for Psych soon, so I won't be around much longer.
    By the second fundamental theorem of calculus, if g(x) = \int_0^x f(t)~dt it means that g'(x) = f(x), that is, the function f is the derivative of the function g. so to get g, integrate all the pieces of f
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