Which of the following equations is the formula of f(x) = x^{1/3} but shifted 2 units to the right and 2 units down?

Question

Which of the following equations is the formula of f(x) = x^{1/3} but shifted 2 units to the right and 2 units down?

A. f(x) = 2x^{1/3} -2
B. f(x) = (x-2)^{1/3} -2
C. f(x) = 2x^{1/3} +2
D. f(x) = (x+2)^{1/3} -2

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Brielle 2 weeks 2021-11-21T12:44:37+00:00 1 Answer 0

Answers ( )

    0
    2021-11-21T12:46:11+00:00

    Answer:

    f(x)=(x-2)^{\frac{1}{3}}-2 ⇒ answer B

    Step-by-step explanation:

    * Lets revise some transformation

    – If the function f(x) translated horizontally to the right  

     by h units, then the new function g(x) = f(x – h)

    – If the function f(x) translated horizontally to the left  

     by h units, then the new function g(x) = f(x + h)

    – If the function f(x) translated vertically up  

     by k units, then the new function g(x) = f(x) + k

    – If the function f(x) translated vertically down  

     by k units, then the new function g(x) = f(x) – k

    * Now lets solve the problem

    ∵ f(x) = x^1/3

    – f(x) shifted 2 units to the right

    ∴ f(x) = (x – 2)^1/3

    – f(x) shifted 2 units down

    ∴ f(x) = (x – 2)^1/3 – 2

    * f(x)=(x - 2)^{\frac{1}{3}}-2

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