Question

Graph |y| < 1 how can I graph this? Please explain

Answer 1

first off, let's keep in mind that an absolute value expression is really a duet rolled in one, so we really have a plus and a minus version of the same thing, so

`|y| < 1\implies \begin{cases} +y < 1\\\\ -y < 1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +y < 1\implies \boxed{y < 1}\hspace{9em}-y < 1\implies \boxed{y > -1}`

so that's what we graph, so if we go to their "linear counterpart", the line itself is simply y = 1 and y = -1, a horizontal line in each case, because the border line is not part of the inequality, the line will be dashed, y > 1 for example means, "y is greater than 1" is not 1 ever, is greater than 1, so the borderline is not part of the inequality.

Check the picture below.