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The function g(x) is a transformation of the cube root parent function,
f(x)=√. What function is g(x)?
-5
1
5
f(x)
g(x)
O
5
1
1
A. g(x)=√x +4-3
OB. g(x)=√x-3-4
C. g(x)=√x + 3-4
D. g(x)=√x-4-3

The Function Gx Is A Transformation Of The Cube Root Parent Function Fx What Function Is Gx 5 1 5 Fx Gx O 5 1 1 A Gxx 43 OB Gxx34 C Gxx 34 D Gxx43 class=

Sagot :

facundo3141592

We have a translation 3 units downwards and 4 units to the right. So the equation is:

g(x) = ∛(x - 4) - 3

What is the equation for the function g(x)?

We know that g(x) is a transformation of the parent cube function, which is f(x) = ∛x

If we look at the image, we can see that the graph of g(x) is exactly like the graph of f(x), but translated 3 units downwards and 4 units to the right.

A vertical translation of N units is written as:

g(x) = f(x) + N

  • if N > 0, the translation is upwards.
  • If N <0, the translation is downwards.

A translation of 3 units downwards is written as:

g(x)= f(x) - 3

A horizontal translation of N units is written as:

g(x) = f(x + N)

  • if N > 0, the translation is to the left.
  • If N <0, the translation is to the right.

Then a translation of 4 units to the right is:

g(x) = f(x - 4) - 3

Replacing the function f(x) we get:

g(x) = ∛(x - 4) - 3

That is the transformed function. So the correct option is D

If you want to learn more about transformations:

https://brainly.com/question/4289712

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