Question

Which of the following equations is the formula of f(x) = x^1/3 but shifted 4 units to the left and 4 units up?

A.
`f(x) = (x-4)^(1/3) +4`
B.
`f(x) = 4x^(1/3) -4`
C.
`f(x)=(x+4)^(1/3) +4`
D.
`f(x) = 4x^(1/3) +4`

Answer 1

C

Explanation:

For a function f(x) =
`x^{(1)/(3)}`, we have:

• f(x) =
  `(x-b)^{(1)/(3)}` is original translated b units right
• f(x) =
  `(x+b)^{(1)/(3)}` is original translated b units left
• f(x) =
  `x^{(1)/(3)}+c` is original translated c units up
• f(x) =
  `x^{(1)/(3)}-c` is original translated c units down

Keeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation
`f(x)=(x+4)^{(1)/(3)}+4`

correct answer is C

Answer 2

Hence correct chcie is C.

`f\left(x\right)=(x+4)^{(1)/(3)}+4`

Explanation:

Given function is
`f\left(x\right)=x^{(1)/(3)}`

Now it says that function is shifted 4 units to the left and 4 units up.

We need to find about which of the given choice is correct for the given transformation.

When f(x) is shifted "h" units left then we write f(x+h)

So
`f\left(x\right)=x^{(1)/(3)}` will change to

`f\left(x\right)=(x+4)^{(1)/(3)}`

When f(x) is shifted "h" units up then we write f(x)+h

So
`f\left(x\right)=(x+4)^{(1)/(3)}` will change to

`f\left(x\right)=(x+4)^{(1)/(3)}+4`