1 - Algebra and functions

1. DEFINED
   1. ALL ELEMENTS
2. EITHER
   1. ONE-ONE
   2. MANY-ONE

1. fg(x)
   1. g(x)
      1. f(g[x])

1. ONE-ONE
2. DOMAIN = RANGE

   Annotations:

   • DOMAIN OF f^-1 = RANGE OF f
3. RANGE = DOMAIN

   Annotations:

   • RANGE OF f^-1 = DOMAIN OF f
4. CHANGE SUBJECT

   Annotations:

   • MAKE x SUBJECT; THEN REWRITE "SWAPPING" x 's AND y 's (OR f(x) 's)

Annotations:

• y = f(x) + a translation by a units in y-direction
• y = f(x + a) translation by -a units in x-direction

Annotations:

• y = a f(x) stretch by scale factor a in y-direction
• y = f(a x) stretch by scale factor 1/a in x-direction

Annotations:

• y = -f(x) reflection in x-axis
• y = f(-x) reflection in y-axis