C3

1. graph
   1. |f(x)|

      Anmerkungen:

      • draw normally, flip up the negatives. always label
   2. f(|x|)

      Anmerkungen:

      • ignore left side, draw over it with the reflection of the right side
2. solve simultaneous modulus equations

1. mapping diagrams
2. one to one, one to many

Anmerkungen:

• calc by reversing subject (make x the subject, not f(x))

1. reverses domain / range
2. mirrors in y=x

1. transforming them
   1. outside y, inside x
   2. y truths, x lies
   3. x / stretch and squish, + - shift
2. sketching
   1. axis crossing points

      Anmerkungen:

      • cross x axis, y=0
      • cross y axis, x = 0
   2. asymptotes
   3. turning points

      Anmerkungen:

      • \(\frac{dy}{dx}=0\)

1. e, asymptote y=0, crosses (0,1)
2. ln, asymptote x=0, crosses (1,0)
3. all kinds of e^x powers
   1. incl. e^-x

Anmerkungen:

• can be to any power of it too

1. essentially the inverse to e^x

Anmerkungen:

• \[cos^{2}A + sin^{2}A \equiv 1\]
• \[sec ^{2}A \equiv 1 + tan^{2}A\]
• \[cosec^{2}A \equiv 1 + cot^{2}A\]

1. prove them

1. graphs of all
2. when are they 0? 1? asymptote?
3. the inverses are 1/whatever

1. cancelling down
2. +, -, x, /