The Kaiser said:
I'm not sure if this is in the right section but I have always been wondering about the style and depictions of the graphs [y = x^x, y= x^(x^2) or xlogx, y= f(x)^f(x) and vise versa] could someone please sketch or describe it to me if they have the time.
Thks in advance.
I direct you here to an excellent graphing utility:
http://www8.pair.com/ksoft/
Otherwise (all curves have y=e^x as reference):
y=x^x like e^(x^x) but 'larger'.
y=e^(x^x)
y=(e^x)^x = e^(x^2)
y=(e^x)^(e^x) = e^(xe^x)
y=sin(x)^sin(x) (with sin(x) reference... hehe curly moustache)
y=tan(x)^tan(x)
y=ln(x)^ln(x)
y=ln(ln(x)) is boring. It just looks like ln(x) translated down and to the right. In fact, as a general rule, taking the logarithm of anything is very boring (typically looks like either ln(x) or the original graph). y=1/ln(f(x)) can give some semi-interesting graphs.
Interestingly, sqrt(f(x))^sqrt(f(x)) seems to barely change the graph's shape compared to f(x)^f(x), aside from domain restriction to positives, similar to taking sqrt(f(x)). Probably because as an exponential it is: y=(f(x))^((f(x)^(1/2))/2),
