robert7248
contestada

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. [tex]f(x) = (x-4)^{1/3} +4[/tex]
B. [tex]f(x) = 4x^{1/3} -4[/tex]
C. [tex]f(x)=(x+4)^{1/3} +4[/tex]
D. [tex]f(x) = 4x^{1/3} +4[/tex]

Respuesta :

lublana

Answer:

Hence correct chcie is C.

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]

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 [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]

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

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

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

TaeKwonDoIsDead

Answer:

C

Step-by-step explanation:

For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:

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

correct answer is C

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