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?

Answer 1

Answer:

C

Step-by-step explanation:

For a function f(x) = $x^{\frac{1}{3}}$, we have:

• f(x) = $(x-b)^{\frac{1}{3}}$ is original translated b units right
• f(x) = $(x+b)^{\frac{1}{3}}$ is original translated b units left
• f(x) = $x^{\frac{1}{3}}+c$ is original translated c units up
• f(x) = $x^{\frac{1}{3}}-c$ 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  $f(x)=(x+4)^{\frac{1}{3}}+4$

correct answer is C

Answer 2

Answer:

Hence correct chcie is C.

$f\left(x\right)=(x+4)^{\frac{1}{3}}+4$

Step-by-step explanation:

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

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 $f\left(x\right)=x^{\frac{1}{3}}$ will change to

$f\left(x\right)=(x+4)^{\frac{1}{3}}$

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

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

$f\left(x\right)=(x+4)^{\frac{1}{3}}+4$