Pre-Cal 40S March 4, 2009

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Vertical and horizontal reflections and inverse functions.

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Pre-Cal 40S March 4, 2009

  1. 1. Baby Play or All About Inverse Functions duck wrangling by toyfoto
  2. 2. Are these functions even or odd? Justify your answers algebraically. 3 g(x) = x + 3x 4 ƒ(x) = x + 2x + 3 2
  3. 3. ƒ is an even function. COMPLETE THE GRAPH.
  4. 4. ƒ is an odd function. COMPLETE THE GRAPH.
  5. 5. Reflections I thought I saw a puddy cat.... by flickr user law_keven
  6. 6. Reflections Vertical Reflections Given any function ƒ(x): • ƒ(x) produces a reflection in the x-axis. y-coordinates are multiplied by (-1) Horizontal Reflections Given any function ƒ(x): • ƒ(-x) produces a reflection in the y-axis. x-coordinates are multiplied by (-1) Inverses: the inverse of any function ƒ(x) is (read as: quot;EFF INVERSEquot;) WARNING: undoes whatever ƒ did. Zuiderkerk by flickr user MorBCN
  7. 7. Reflections Vertical Reflections Given any function ƒ(x): • ƒ(x) produces a reflection in the x-axis. y-coordinates are multiplied by (-1) Horizontal Reflections Given any function ƒ(x): • ƒ(-x) produces a reflection in the y-axis. x-coordinates are multiplied by (-1) Inverses: the inverse of any function ƒ(x) is (read as: quot;EFF INVERSEquot;) WARNING: undoes whatever ƒ did. Zuiderkerk by flickr user MorBCN
  8. 8. Baby Play or All About Inverse Functions duck wrangling by toyfoto
  9. 9. Inverses ... The concept ... Numerically speaking ...
  10. 10. Inverses ... Conceptually analyzing Algebraically speaking ... the function ...
  11. 11. Inverses ... Graphically speaking ...

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