Why does Desmos not render graphs like this properly?

Question

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

Presumably it's only working to finite precision and just not calculating the relevant values of $x$. You can figure out what those values are by substituting $y = 40$ and solving for $x$. — Qiaochu Yuan, Sep 15 '23 at 21:40
Indeed the relevant value of $x$ is about $2.32\times*10^{-16}$ less than $2$, which is right around machine precision. — Greg Martin, Sep 15 '23 at 21:41

score 5 · Accepted Answer · answered Sep 15 '23 at 22:12

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:

Sometimes the calculator detects that an equation is too complicated to plot perfectly in a reasonable amount of time. When this happens, the equation is plotted at lower resolution.

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.

Thank you for this and for the term, will know what to say when students ask this again. — PhysicsMathsLove, Sep 15 '23 at 22:17

Why does Desmos not render graphs like this properly?

1 Answers1