I tried to figure out if this graph exists, but I don't know if I am thinking this right. The absolute value of $x$ is always positive and the minus in front of the absolute value of $x$ makes it always negative. So my final conclusion is that it does not exist but I am not sure of this.
2026-04-18 18:00:31.1776535231
Does the graph of $\ln(-2 - |x|)$ exist?
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If it's only real numbers you're working with, then no. If you're familiar with complex logarithms then $\log(z)=\log|z|+\mathrm{i}\theta$ might help, where $\theta$ is the argument of $z$.