Graph with exponent not correct

[Dieter]

(10-26-2017 05:45 PM)MullenJohn Wrote:  When I graph the function (X^2 - 4)^(2/3) on the HP Prime there is nothing showing between -2 and +2. (This also happens on my HP 50g calculator)

However when I rearrange the function to the form 3√(x^2-4)^2/3 the graph display properly between -2 and +2.

First of all, I assume you mean the cube root of (x²–4)² here.

Between –2 and +2 the value for x²–4 becomes negative, e.g. for x=0 it is –4. Now, what is –4^(2/3)? There is no real result, the answer is –1,2599+2,1822 i, a complex number. This cannot be shown in a graph with a real y-axis only.

On the other hand the second way of writing the formula causes less problems: (x²–4)² is always positive (or at least zero). So the cube root can be calculated easily. But this is not exactly the same as the first formula.

Finally there is another pitfall: Fractional powers of a negative base usually cause problems. This is because – maybe except in exact mode – the calculator takes the numeric 12-digit value 0,66666 66666 67. Which is not 2/3 but only an approximation, so the root is not defined.

Dieter