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Math Help - Using transformations to write a function?

  1. #1
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    Using transformations to write a function?

    The function f, represented by f(x)=122.8x+786.2, models the average tuition at public four-year colleges from 1981 to 1994, where x is the year and x=1 corresponds to 1981. Use transformations to determine a function g that computes the average tuition at four-year colleges during the year x, where x is the actual year.

    Need some guidance please?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by moomoo762 View Post
    The function f, represented by f(x)=122.8x+786.2, models the average tuition at public four-year colleges from 1981 to 1994, where x is the year and x=1 corresponds to 1981. Use transformations to determine a function g that computes the average tuition at four-year colleges during the year x, where x is the actual year.

    Need some guidance please?
    Jus put 1981 at the place where x=1. I.E. relable your axis.
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  3. #3
    Super Member malaygoel's Avatar
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    We can assume that g is a linear transform of f.

    hence g=Af+B
    where A,B are transformation constants.

    Now determine A,B

    Spoiler:


    g(x)=Af(x)+B

    by definition of g,
    f(1)=g(1981)=Af(1981)+B
    by definition of f
    f(1)=122.8(1)+786.2

    hence,
    Af(1981)+B=122.8(1)+786.2........(1)

    Similarly,
    Af(1982)+B=122.8(2)+786.2.........(2)

    subtracting (1)from (2)
    A(f(1982)-f(1981))=122.8
    hence, A=1
    B=243144

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