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Rewrite 3√27x−81−5 to make it easy to graph using a translation. Describe the graph.
7 answers
Is anyone there? I need help!
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
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
@oobleck, the question was actually
_____
³√27x-81 -5
but I am confused myself.
_____
³√27x-81 -5
but I am confused myself.
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.
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.
True
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.
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.