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Math Help - Defining functions.... True or False

  1. #1
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    Defining functions.... True or False

    Answer true of false to the following questions:

    1. It is possible to uniquely define a quadratic function given 4 distinct points.

    2. It is possible to uniquely define a constant function given 4 distinct points.

    3. It is possible to uniquely define a quartic function given 4 distinct points.

    4. It is possible to uniquely define a cubic function given 4 distinct points.

    5. It is possible to uniquely define a quintic function given 4 distinct points.
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  2. #2
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    Quote Originally Posted by trae View Post
    Answer true of false to the following questions:

    1. It is possible to uniquely define a quadratic function given 4 distinct points.

    2. It is possible to uniquely define a constant function given 4 distinct points.

    3. It is possible to uniquely define a quartic function given 4 distinct points.

    4. It is possible to uniquely define a cubic function given 4 distinct points.

    5. It is possible to uniquely define a quintic function given 4 distinct points.

    The answer would be TRUE to all if you are asking if it is possible for at least one set of 4 distinct points.

    However, if you are asking if it is always possible to define a function such functions:

    1,2,3,5 are all false, but 4 is true .
    Think of the general polynomial equation and the number of constants you have to solve for
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  3. #3
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    isnt 2 true?
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    Quote Originally Posted by finch41 View Post
    isnt 2 true?
    "Is it always possible to uniquely define a constant function given 4 distinct points"?
    No. Because 1 point fixes the constant function.
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