Hi can anyone help me sketch the shape of the graph X^X .

Thank you

Umm, do you mean X to the power of X? wouldnt you just make it y = x^x so if x = 0

then y = 0^0, x=1 then y = 1^1, then x =2 y = 2^2, if x = 3 then y = 3^3?

hey it's easy to just say it. try drawing it. For negative powers it gets really confusing

Are you aware that the negative exponents are just the inverses of the corresponding positive exponent (for even x's) and the negative inverse of the corresponding positive exponent (for odd x's)?

 

X=-2 ----- You know that 2^2=4 so -2^-2 is 1/4

 

X=-3 ----- You know that 3^3=27 so -3^-3 is -1/27

Because:

 

-2^-2

=

1 / -2^2

=

1 / 4

(because -2 x -2 (two negatives make a plus!) so 4)

the graph of x^x is weird. its alrite for positive values of x. not defined at 0, but tends to 1 as x tends ti 0 from the right. its alrite for negative integers. but for negative numbers like -1/2. we have (-1/2)^(-1/2) . which is is 1 over the square root if a negative number. which is not it ]R

Yeah, I forgot about all the fractions and stuff. My initial thoughts were to use complex numbers and graph it with those but then I figured that was propably too complicated so I just stuck to integers. Don't know why I didn't think of fractions.

 

So if we used complex numbers, it would just have an asymptote at y=0, assuming the equation is z=x+iy?

It seems that even a few programs can't plot the curve.( see attachment)

so wat is the shape of the graph? atleast a rough sketch

?

 

You can't draw a graph for it for negative x; there's just too many discontinuities.