Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Rewrite 3√27x−81−5 to make it easy to graph using a translation. Describe the graph.

Over 1800 ppl saw this and no one knows the answer...

numbers 27 and 81 have 27 as common factor which is equal to 3^3. Noting that we can put 27 before brackets write it in form 3^3 and that third root and cube will trim.

3sqrt 27x-81-5=
3sqrt 27(x-3)-5=
3sqrt 3^3(x-3)-5=
3 3sqrt x-3-5

-5 means that graph is shifted 5 to down.
-3 means it is shifted to right by -3
3 and ∛ represent scaling of graph which can be seen and tested once you draw it. It is harder to explain it with words.

You need to learn to use parentheses online to make things clear. Since this is an exercise in translation, I assume you meant

3√(27x-81) - 5
= 3√(27(x-3)) - 5
= 9√3 (x-3) - 5
So, if f(x) = √x, this one is f(x) transformed as follows:
shift right 3
dilate y by a factor of 9√3
shift down 5

Is anyone there? I need help!

@oobleck, the question was actually

_____
³√27x-81 -5
but I am confused myself.

I apologize for misunderstanding the question at first. Your initial statement was correct.

Given ³√27x-81 -5, we can simplify it as follows:

³√27x-81 -5 = ³√(27(x-3))) - 5 = ³√(3³(x-3)) - 5 = 3√3(x-3) - 5

This is a radical function of the form f(x)= k√x + c, where k= 3√3 and c= -5.

To graph, start with the parent function y=√x, which has a square root behavior. Then, apply the transformations as follows:

- Shift the function to the right by 3 units. This is done by replacing x with x-3 in the parent function, so the function becomes y=√(x-3)
- Vertically stretch the function by a factor of 3√3. This will make the slope of the curve steeper.
- Shift the curve downward by 5 units.

The final function is y= 3√3(x-3) - 5.

True