desmos
I was trying to show some students the graph of $y=4- \ln (2-x)$ today on Desmos.
Unfortunately we can see from the picture below that the graph does not render correctly around the asymptote and appears to 'stop' at around $y=40$. This same behaviour happens when we try to plot the graph on a graphical calculator so I wonder what it is about this graph that is causing this?
Thanks
It appears that your graph was generated using Desmos.
When you click on the solid straight line at the point $x=2$, Desmos does explicitly say that the point is undefined, and exhibits it as a hollow “excluded point” (removable singularity).
I'm unfamiliar with why Desmos shows the exclusion only upon clicking. Maybe there is a software setting that can display them, by default.
On Desmos on my browser the graph of $(-1)^x$ fluctuates between plotting barely any points, one almost completely filled in line, and two almost completely filled in lines depending on the width of my browser window. Unfortunately when I tried to show this off in class on another similar computer I wasn't able to get anything to show up (it probably depends on screen resolution!)
Roughly speaking, Desmos breaks up the $x$-axis of the viewing window into a bunch of discrete, evenly spaced points, probably one for each pixel, and plugs those values into the function. Desmos is perfectly happy to take some random decimals and plug them into $(-1)^x$, such as:
This seems to be based on reduced fraction representations of the decimals:
Depending on which specific decimals Desmos chooses to plug in, you'll get different looking graphs.
Best Answer
Like (almost) everything, Desmos is not perfect.
The "term" for this is unresolved detail, as Desmos calls it. This is what an official Desmos FAQ officially says about this:
For more on Desmos, I answered a similar question here. Also, here is a slightly less trusted website (Reddit) but it does have a great example of what you were experiencing.