I had a question to plot a graph of
$\space \space\LARGE y=x^{x^{x^{x^{...}}}}$
Which (according to me) is equivalent to
$\large y=x^y \Rightarrow y^{\frac{1}{y}}=x$
So i plotted them in my copy (by taking dozens of different values of y to get x)
To check my graph i plotted them in both "DESMOS" and "WOLFRAMALPHA"
The Results:
Desmos: (Same as mine!) 
WolframAlpha:
Why does the graph in the case of WolframAlpha going towards $-x$-axis?
On
This is not an answer but it is too long for a comment.
If you are concerned by the plot of $y$ as a function of $x$ such that $\space y^{1/y}=x$, it means that $$y=-\dfrac{W(-\log (x))}{\log (x)}$$ where appears Lambert function.
In the real domain, $x$ must be positive and function $W(a)$ is only defines if $a \geq -\frac 1e$ which makes $0 < x \leq e^{\frac{1}{e}}\approx 1.44467$ and $y$ varies between $0$ and $e$. At both ends, the tangent to the curves is vertical.
May I suggest you ask Wolfram Alpha to plot the equation I wrote and I suppose that you will get something similar to what you obtained with your own plot.
The Wolfram Alpha one doesn't seem to start at $ x=0 $ (look at the numbers at the bottom).