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Thread: How could one write an expression/'function' for these graphs?

  1. #1
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    How could one write an expression/'function' for these graphs?

    Here are some graphs that I am aware are not technically functions.


    How could one write an expression/'function' for these graphs?-2.png

    I am trying to write 'functions' for them

    My attempt:

    A. Maybe I could write something like $\displaystyle x = n \forall n \in \mathbb{N}$ and $\displaystyle 0 \leq y \leq 1$. I don't know if this is a valid way to define a 'function'? Clearly if this is right then for B. the range for y could just be extended.

    C. This should be something like $\displaystyle y^2 = x$ but repeating every 1, and I'm not sure how I can do this.

    Thanks in advance for your help.
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  2. #2
    MHF Contributor
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    Re: How could one write an expression/'function' for these graphs?

    Hey kinhew93.

    Functions don't satisfy that property since a function has to only be defined to have one value for all input combinations.

    So if you take an input combination [call it a vector V] then if f(V) has two possibilities it is not a function.

    All of your above graphs are not a function if you try to use y = f(x).
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