Graph of $|y|=|\log(1-|x|)|$

Question

To draw the graph of $|y|=|\log(1-|x|)|$, I see that $x=0, y=0$ satisfies it. Also, the asymptotes would be $x=1, x=-1$. I have made a graph which has sort of eight curves in it but I don't know how to show that here. Can anyone draw a graph here so that I could verify if what I have drawn is correct or not. Thanks.

Answer 1

You can enter implicit graphs in Desmos: https://www.desmos.com/calculator/mnzugobjqu

To figure out what this looks like by hand, experiment in Desmos with adding and removing the absolute value signs to see how each affects the graph $y = \log(1-x)$.

Answer 2

We can write this as $y= log(1- |x|)$ and $y= -log(1- |x|)$.

Now take the absolute value off x:

1. $y= log(1- x)$ for $x\ge 0$ Of course, log(1- x) is only defined for $1- x> 0$ so $0\le x< 1$.

2. $y= log(1+ x)$ for $x< 0$ Of course, log(1+ x) is only defined for $1+ x> 0$ so $-1< x\le 0$.

3. $y= -log(1- x)$ for $xge 0$ Of course, log(1- x) is only defined for $1- x> 0$ so $0\le x< 1$.

4. $y= -log(1+ x)$ for $x< 0$. Of course, log(1+ x) is only defined for $1+ x> 0$ so $-1< x\le 0$.