What radical function is represented in the graph?

F(x)=?

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  • ?
    Lv 7
    1 month ago

    This is a graph of y = ∛x = x^⅓  SHIFTED RIGHT by 2 units, and shifted DOWN by 1 unit. The equation of the new function is

    ......................F(x) = (x-2)^⅓  - 1...................ANS

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  • It's going to be related to the form of f(x) = x^(1/(2n + 1))

    If it was f(x) = a * (x - h)^(1/3) + k, then we can probably express it easily enough.  It looks like (h , k) is at (2 , -1)

    f(x) = a * (x - 2)^(1/3) - 1

    f(3) = 0

    0 = a * (3 - 2)^(1/3) - 1

    0 = a * 1^(1/3) - 1

    1 = a * 1

    1 = a

    f(x) = (x - 2)^(1/3) - 1

    What if it was f(x) = a * (x - h)^(1/5) + k?  Again, if we said that (h , k) is (2 , -1), we can solve for a

    f(x) = a * (x - 2)^(1/5) - 1

    f(3) = 0

    0 = a * (3 - 2)^(1/5) - 1

    1 = a * 1^(1/5)

    1 = a

    It seems that we can have an infinite number of functions that would work

    f(x) = (x - 2)^(1/(2n + 1)) - 1, where n is a positive integer

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