Odd function effect in desmos Graph in desmos
(Zoom in on its negative side starting at x=-30)
Why is it choppy? 
Why does it stop at x=-35.63?
Desmos:

Symbolab:

Is it just that the graphers can't handle it?
Thanks in advance.
 A: You will see a helpful clue if you instead plot $\log_2\mathopen{}\left(\sqrt{e^x+1}-1\right)\mathclose{}$, which maybe you need to enter in Desmos as $\ln\mathopen{}\left(\sqrt{e^x+1}-1\right)\mathclose{}/\ln(2)$.
The output values are then $\{-52,-51,-50.4\ldots,-50,\ldots\}$. 
I would deduce that Desmos treats real numbers as having 52 bits past the decimal and no more. So for large enough negative $x$ (Apparently close to $-35$) you have in binary that $$\sqrt{e^x+1}-1\approx0.\overbrace{0\ldots01}^{52\text{ bits}}$$ and the $\log_2$ gives $-52$. 
Then as far as Desmos is concerned, the next largest real number is $0.\overbrace{0\ldots010}^{52\text{ bits}}$, and $\log_2$ returns $-51$. And then the next largest real number is $0.\overbrace{0\ldots011}^{52\text{ bits}}$, and $\log_2$ returns $-50.4\ldots$.
So you are seeing Desmos have to round to discrete values on the order of $2^{-52}$. Furthermore, once $x$ is just a bit beyond $-35$, then Desmos has to round $$\sqrt{e^x+1}-1\approx0.\overbrace{0\ldots00}^{52\text{ bits}}$$ and now the logarithm will give no output at all.

Once you understand this issue, you can use expressions that are algebraically equivalent but will not ask Desmos to compute at that order of magnitude. Here, you can replace $\ln\mathopen{}\left(\sqrt{e^x+1}-1\right)\mathclose{}$ with the equivalent $x-\ln\mathopen{}\left(\sqrt{e^x+1}+1\right)\mathclose{}$. When I do so, now I have a smooth-looking graph in the negative direction forever. (It cuts off quickly in the positive direction, but some kind of if/then definition of the function, using one expression for positive $x$ and another for negative $x$ should work in both direction.)
A: The problem lies in the second term of your function, being $ln(\sqrt{e^x+1}-x)$. What happens is, that if $x$ becomes negative, that e-power rapidly goes to zero. What happens then, is that you are asking the program to take the ln of a number so incredibly close to zero, that the arithmetic part can't handle it. When I type in $e^{-35}$ in my TI, and add $1$ and take square root, it flatly gives me $1$, which is of course not right either. So DESMOS is not the only program struggling here. Best thing is to combine the ln terms and simplify (to plainly $x$)and regraph. DEMSOS has no issues then. Technology is great but has limitations...
