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Math Help - Plotting graphs in C[a,b]

  1. #1
    Senior Member bugatti79's Avatar
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    Plotting graphs in C[a,b]

    Folks,

    If given p =3 and q=6 any numbers and the set \{f \in \mathbb[C} [a,b]: p\ge f(x) \le q \forall x \in [a,b]\}

    Is my graph of f(x)=x^3 +3 shown in this wolfram link correct based on this set?

    plot y(x)=x^3+3 between 3 and 6 - Wolfram|Alpha


    1) What norm is this C[a,b] is representing...is it a sup norm, taxi cab norm?

    2) What is the effect if the C[a,b] with sup norm is required?

    Thanks
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  2. #2
    MHF Contributor

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    Re: Plotting graphs in C[a,b]

    The sup norm is the standard norm on C[a,b] (the set of functions continuous on the interval [a, b]).
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  3. #3
    Senior Member bugatti79's Avatar
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    Re: Plotting graphs in C[a,b]

    Quote Originally Posted by HallsofIvy View Post
    The sup norm is the standard norm on C[a,b] (the set of functions continuous on the interval [a, b]).
    Ok, another question suppose I have \{f,g \in \mathbb{C} [a,b]: p\ge || f(x)-g(x)|| \le q \forall x \in [a,b]\}

    How would I plot this assuming we know the functions ie, f(x)=x^3+3 and g(x)=x-1. Will the sup norm norm involve max{|f(x)|,|g(x)| for plotting?

    Thanks

    Also posted here but will keep each forum informed of responses. Thanks
    Functions in Normed Linear Space
    Last edited by bugatti79; December 8th 2011 at 08:53 AM.
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