1 - Algebra and functions

1 - Algebra and functions

1. DOMAIN

2. RANGE

3. MAPPING

   • ONE-ONE
   • MANY-ONE
   • ONE-MANY
   • MANY-MANY

4. FUNCTION

   • CONDITIONS
     • DEFINED
       • ALL ELEMENTS
     • EITHER
       • ONE-ONE
       • MANY-ONE
   • COMPOSITE
     • fg(x)
       • g(x)
         • f(g[x])
   • INVERSE
     • ONE-ONE
     • DOMAIN = RANGE
       • DOMAIN OF f^-1 = RANGE OF f
     • RANGE = DOMAIN
       • RANGE OF f^-1 = DOMAIN OF f
     • CHANGE SUBJECT
       • MAKE x SUBJECT; THEN REWRITE "SWAPPING" x 's AND y 's (OR f(x) 's)

5. TRANSFORMATIONS

   • TRANSLATIONS
     • y = f(x) + a translation by a units in y-direction
     • y = f(x + a) translation by -a units in x-direction
   • STRECHES
     • 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
   • REFLECTIONS
     • y = -f(x) reflection in x-axis
     • y = f(-x) reflection in y-axis

6. MODULUS

   • POSITIVE

7. EXPONENTIAL

   • e
   • ln