If $Y$ is a transformation of $X$, then why is it that $|f_X(x) dx| = |f_Y(y) dy|$ instead of simply $f_X(x) dx = f_Y(y) dy$? This should be an intuitively easy question but I'm trying to think of an example for when this would be the case. Is it because $dy$ could "intuitively" be negative? For example, the mapping from $X$ to $-X.$
I just need some clarification here. Thanks!