Sketching x^n where n is a fraction...how?

[ZachCharge]

Hail,

So we have a SAC on trig and composite functions Thrusday/Friday this week. Today our teacher sorta slipped out transformations of functions of where n is a fraction. The only problem is, we only touched this in class weeks ago and my notes on it are not up to scratch. Math Quest as expected does not mention these. Anyone have any documentation that explains how to go about these?
Must remain third...must remain third...or higher


Thanks in advance.

[|ll|lll|]

What kind of fractions are you looking at?

Basically, if n = 1r2, the graph would be a square root graph.
When n = 1r3, the graph would be a cube root graph and so on.
Try negative fractions on your CAS too...

However, I can't help much because I haven't learnt composite functions yet.
Good luck nevertheless

[cameron_15]

n^1/2 is the square root function, which is half a parabola on its side.



n^1/3 is the cube root funtion, which is a cubic graph on its side (sort of).



They should be the only ones you get...

...and very soon someone awesome at maths is going to give you a way better summary thing of this in a few minutes...

[|ll|lll|]

^ Lol yeah, maybe.

For the graph y = x^(1r3), it's actually the graph of the inverse function of y = x^3.
So for y = x^(1r n ), just think of the inverse of the function y = x ^ n

[the.watchman]

^ Lol yeah, maybe.

For the graph y = x^(1r3), it's actually the graph of the inverse function of y = x^3.
So for y = x^(1r n ), just think of the inverse of the function y = x ^ n

EXCEPT anything with an even denominator, in which only the positive side is taken
And also, fractions with even numerators have both portions to the graph, eg. x^{2/5} and x^{4/3}

[ZachCharge]

Thanks for the help, now I don't feel lost.

[m@tty]

EXCEPT anything with an even denominator, in which only the positive side is taken

Oh yeah, my bad Because it's not defined when you take the even-number root of a negative integer

Not defined over ..

Also it is worth noting that if n has both an even numerator and denominator, two arms are present, both positive and negative, even(lol) though it simplifies to a function with a normally narrower domain.

Eg . So it is the normal square root graph, BUT it's domain is (not ).

[Mao]

Eg . So it is the normal square root graph, BUT it's domain is (not ).

Really? Do you have sources?

Fractional powers are open to interpretation, so do I take the interpretation that or ? The prior would suggest you are right, the latter would suggest you are wrong.

Or, to generalise, do we always accept ?

[naved_s9994]

Eg . So it is the normal square root graph, BUT it's domain is (not ).

I dont think thats the case either, from memory...
Its in the methods textbook (essentials), somewhere Ch 1-4  : Dont have the book on me atm, otherwise, i would have directly reffered you..