# 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?

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

You mean there is a discontinuity?

prasannapakkiam
Yes I suppose you could call it that

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

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!