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# What radical function is represented in the graph?

F(x)=?

### 2 Answers

- ?Lv 71 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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- 1 month ago
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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