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Math Help - [SOLVED] Combining functions

  1. #1
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    [SOLVED] Combining functions

    Given the graph of a function with a few clear ordered pairs. Call it f(x). Can one use those given points on the graph, to sketch (f+f)(x)? Add y values? Add x values? Both?
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    Quote Originally Posted by EyesForEars View Post
    Given the graph of a function with a few clear ordered pairs. Call it f(x). Can one use those given points on the graph, to sketch (f+f)(x)? Add y values? Add x values? Both?
    double the y-values (the second coordinate in each pair). do you see why this works?
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    Honestly no. I wish I could. The coordinates are (-2,2.5)(-1,2)(0,1.5)(1,1)(3,-1) So when you say double, do you mean multiply? So that last coordinate would be (3,-2)? Also, i don't know if it matters, but just looking at it i can tell you its a piecewise. Its linear for the first four points, then it turns curvelinear from (1,1) to (3,-1)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by EyesForEars View Post
    Honestly no. I wish I could. The coordinates are (-2,2.5)(-1,2)(0,1.5)(1,1)(3,-1) So when you say double, do you mean multiply?
    yes, double means multiply by two. do you realize that (f + f)(x) = f(x) + f(x) = 2f(x)...or in other words, 2 times the y-value.

    So that last coordinate would be (3,-2)?
    yes

    Also, i don't know if it matters, but just looking at it i can tell you its a piecewise. Its linear for the first four points, then it turns curvelinear from (1,1) to (3,-1)
    no, we cannot tell from this. we just have discrete points here. descriptions like "piece-wise" do not apply. if these points are just a few points given for a non-discrete function, then we cannot tell whether the function is piece-wise or not here.
    Last edited by Jhevon; February 7th 2009 at 08:57 PM.
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    Ah! I think i get it! Tell me if im on the right track. y=ax+b So, if your going to add  ax+b to itself you would get 2ax+2b. Hence,  2f(x) or, 2y?
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    Quote Originally Posted by EyesForEars View Post
    Ah! I think i get it! Tell me if im on the right track. y=ax+b So, if your going to add  ax+b to itself you would get 2ax+2b. Hence,  2f(x) or, 2y?
    Exactly! Operations on functions may look bad, but they're really pretty simplistic. The "(f + f)(x)" means nothing more than "f(x) + f(x)", or "2f(x)". So if f(x) = mx + b, then (f + f)(x) = 2f(x) = 2(mx + b) = 2mx + 2b.

    Good work!
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