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Math Help - what is : "one variable being a function of another.

  1. #1
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    what is : "one variable being a function of another.

    I'm preparing to take an exemption test which will allow me to bypass intermediate/pre-algebra and go into college algebra (math 1111_
    ..one of the stated objectives i should know is:
    "Define the concept of one variable being a function of another."
    - i have the textbook for the course I'm trying to bypass and am grinding away, but thought someone may expand on this concept.
    thank you
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  2. #2
    Super Member Anonymous1's Avatar
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    So we have y=f(x) right... What does this mean?

    x is a number. Think of x in terms of the x-axis; it take on values (-\infty, \infty).

    Then f(x) is a mapping of x. It takes the values of x and transforms them to take on new properties.

    For definiteness:

    we have f(x)=x^2.

    Again x is just the Real line: (-\infty, \infty).

    f(x) on the other hand, takes on the properties of a parabola. Also, it can only yield positive values, so its range is restricted to [0,\infty).

    So as we feed f(x) input values, x, it transforms them to take on these new properties as described above.

    When we set y equal to f(x) we are assigning a variable to the transformed values. So y is a variable that is a function of x.
    Last edited by Anonymous1; April 6th 2010 at 03:25 PM.
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  3. #3
    Super Member Bacterius's Avatar
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    It basically means that one variable is linked to another in a one-way (or possibly bijective) mapping. That is, if variable y is function of x, then choosing a value for x will yield a (or possibly more) value(s) for y by this particular mapping which actually is the function.

    For instance, saying that y is function of x by the function y = x^2, we see that by choosing a value for x, we immediately obtain another value for y which is function of x via this function.

    Does it make sense ?
    I think I confused you more than helped you didn't I
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  4. #4
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by Bacterius View Post
    It basically means that one variable is linked to another in a one-way (or possibly bijective) mapping. That is, if variable y is function of x, then choosing a value for x will yield a (or possibly more) value(s) for y by this particular mapping which actually is the function.

    For instance, saying that y is function of x by the function y = x^2, we see that by choosing a value for x, we immediately obtain another value for y which is function of x via this function.

    Does it make sense ?
    I think I confused you more than helped you didn't I
    I love how we both independently choose f(x)=x^2.
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  5. #5
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    yes, that is the understanding which i initially held....for whatever reason the phrasing
    "Define the concept of one variable being a function of another."

    caused me uncertainty and raised the question: "what did I miss?"...
    thank you both, very clear
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  6. #6
    Super Member Bacterius's Avatar
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    Quote Originally Posted by Anonymous1 View Post
    I love how we both independently choose f(x)=x^2.
    Me too
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