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Math Help - Equations involving modulus function

  1. #1
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    Equations involving modulus function

    Hi, I've been given homework problems from topics that I haven't been taught yet, and I have no idea how to start them, can't find any information in my textbooks Could somebody please explain to me how to go about these problems. They're both similar.

    1) Graph the equation |x| + |y| = 1. Explain whether the graph represents the graph of a
    function of x.

    2) Given f(x) =|x - 1| - |x - 3|
    (a) Draw the graph of f(x).
    (b) Determine the domain and range of f(x).
    (c) Use your graph to solve the inequality |x - 1| - |x - 3| >= 5

    Thanks heaps.
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  2. #2
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    Re: Equations involving modulus function

    Hey Vishak.

    I'll start you off with a hint: For Q1 consider |x| = x if > 0 and -x if < 0 and same for y. You will have four different functions to graph and you can graph them all that fit the criteria.

    Just to be specific, one example is x + y = 1 where x > 0 and y > 0 (both positive).
    Thanks from Vishak
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  3. #3
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    Re: Equations involving modulus function

    Thanks heaps, I think I get it now. Do you know number 2?
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  4. #4
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    Re: Equations involving modulus function

    Try doing the exact same thing and divide the graph when x < 1, x > 1, x < 3 and x > 3.
    Thanks from Vishak
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  5. #5
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    Re: Equations involving modulus function

    Quote Originally Posted by Vishak View Post
    Hi, I've been given homework problems from topics that I haven't been taught yet, and I have no idea how to start them, can't find any information in my textbooks Could somebody please explain to me how to go about these problems. They're both similar.
    1) Graph the equation |x| + |y| = 1. Explain whether the graph represents the graph of a
    function of x
    Have you actually done any web searches? Look at this.
    Thanks from Vishak
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