How to draw $|y|=|(x-2)^2-1|$?

Question

This correspondence's domain and codomain is available for all real numbers. So the codomain and domain are the set of all real numbers on?

And, this graph is true? (This graph was called Wolframalpha 'Implicit plot'. I'm anxious.)

Answer 1

What you have is equivalent to the two functions $y = |(x - 2)^2 - 1|$ and $y = -|(x-2)^2 - 1|$, and is likely called an implicit plot because $|y| = |(x-2)^2-1|$ is not itself a function of $x$. (Note that your graph fails the vertical line test.)

The plot is indeed correct.