I wrote the function y^50=x^2-5x-9.

[prasannapakkiam]

I wrote the function y^50=x^2-5x-9. I found a large gap between the function from the x-axis to the end of the curve. My calculations show that the curve must touch the x-axis. Is this due to the accuracy of the program or does this curve indeed have a gap from the x-axis to the curve?

 

[Werg22]

What is the limit of x^2-5x-9 as x goes to positive infinity?

 

[prasannapakkiam]

Well it tends to Infinity? But I don't see how that helps...

 

[prasannapakkiam]

aaaaaaaa I think there is a misunderstanding.

Okay the graph looks in a way like this like this:

______________________
/
|

--------------------------------x-axis


|
\________________________

the gap is on the left

 

[Werg22]

You mean there is a discontinuity?

 

[prasannapakkiam]

Yes I suppose you could call it that

 

[Werg22]

There is something wrong. There is a discontinuity, since x^2-5x-9 has real roots and hence an interval over which it is negative, but this discontinuity should be between the zeros, on the x-axis that is.

 

[prasannapakkiam]

hmm. So this is due clearly to the accuracy of the program?

As I thought that the range was: yER

 

[Moo Of Doom]

That's just an inaccuracy in the graphing program. The quadratic has 2 real roots, so the function hits zero, and both the quadratic and the fiftieth root function are continuous on their domains, so all the points in between appear as well.

 

[prasannapakkiam]

Thanks for the confirmation.

 

[uart]

Think about this prasannapakkiam, what happens to x^{\frac{1}{50}} when x is close to zero but not exactly zero. Try some examples on your calculator, like 0.001^(1/50) for example.

Remember that your graphing program probably just chooses a bunch of points to evaluate and probably doesn't hit the zeros dead on. Can you see why x^2 - 5x -9 may be very close to zero but (x^2 - 5x -9)^{\frac{1}{50}} not necessarily so!

What I'm saying is this: Yes it is inaccuracy in the program that is causing the effect, but very much relevant to this is the nature of the function in question at points in the neighbourhood of it's zeros.