In the Thomas Calculus Early Transcendentals (Fourteenth Edition in SI units), the vertex of an absolute-value function is included in the domain of the segment with an increasing gradient.
For example: Chapter 1 page 24/25, defines the parent absolute value graph (y = |x|): |x|= x , x ≥ 0 |x| = - x , x < 0
I am struggling to understand how this fits with the definition of an absolute value. Intuitively, the vertex should be included in both domains or neither domain.
Can someone please clarify this for me. Thank you.