What does $f^+:=\max(f,0)$ and $f^-:=\max(-f,0)$ mean

Question

Let $f$ be a continious function over an intervall with
$f^+:=\max(f,0)$ and $f^-:=\max(-f,0)$

What does that mean graphically?

Answer 1

• $f^+$ is equal to
  • $f$ when $f$ is positive
  • $0$ when $f$ is negative
• $f^-$ is equal to
  • $-f$ when $f$ is negative
  • $0$ when $f$ is positive

when plotting $f^+$ and $f^-$ together you will get the same as if you were plotting $g_1$ and $g_2$ with

• $g_1 = |f|$
• $g_2 = 0$