# Geometer's Sketchpad: How to graph x^n?

#### sorbedocs

Hello,

I am using Geometer's Sketchpad and I am trying to display the graph of x^n; that is,

-I have a slider for "n", and so as I move the slider the graph changes (for example if n=2 (a quadratic function), if n=3 (a cubic function)

The PROBLEM that I am having is that in GSP I can graph x^2, and x^3, and so on but as soon as I change the exponent to a variable such as "n", I can only see the values of x that are bigger than or equal to zero (x>=0). In other words, I only get half of the graph, that is, the part of the x>=0 values. I would also like to see the x values that are less than zero (x<0).

How do I get to display this properly?

(See attachment for details. Note: instead of "n" I used "a", same idea though)

Any recommendation, or advice is greatly appreciated.

Sincerely,

SORBEDOCS

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#### jedishrfu

Mentor
The problem is that the graph will oscillate between plus and minus infinity when x<0 as n increases from 0 to some positive integer and it looks like the GSP has similarly restricted all x values to be positive only.

If you use the DESMOS graphing calculator you will see the oscillation as n goes from 0 to 10 in integer step and with n as a real number the x<0 is undefined.

just enter $x^n$ and vary the n value using the slider that appears.

#### fresh_42

Mentor
2018 Award
How do I get to display this properly?
You could mirror the positive branch: at the y-axis for even n, and at the origin for odd n.
But as you can see at @jedishrfu's example on Desmos.com, it would be more interesting to see how only odd or only even powers behave.

"Geometer's Sketchpad: How to graph x^n?"

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