|u|=u for u 0, and |u|=-u for u<0. Thus (x,y) maps to (x,|y|): only negative outputs are reflected in the horizontal axis. Find where the inner line is zero; calculate the vertical intercept when its input is allowed; plot any domain endpoints. Retain the positive branch and reflect the negative one. Read the lowest and highest attained heights. For y=|x+2| on -3 <= x 1, the vertex is (-2,0), endpoints are (-3,1),(1,3), and the range is [0,3]. Check: a restricted graph need not have an axis intersection or range starting at zero. Do not reflect inputs or extend a graph outside its domain.

\(|u|=u\) for \(u\ge0\), and \(|u|=-u\) for \(u<0\). Thus \((x,y)\) maps to \((x,|y|)\): only negative outputs are reflected in the horizontal axis.

Find where the inner line is zero; calculate the vertical intercept when its input is allowed; plot any domain endpoints. Retain the positive branch and reflect the negative one. Read the lowest and highest attained heights.

For \(y=|x+2|\) on \(-3\le x\le1\), the vertex is \((-2,0)\), endpoints are \((-3,1),(1,3)\), and the range is \([0,3]\).

Check: a restricted graph need not have an axis intersection or range starting at zero. Do not reflect inputs or extend a graph outside its domain.

Modulus graphs of linear functions

Modulus graphs of linear functions