Pre-Cal 40S March 1, 2009
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Pre-Cal 40S March 1, 2009

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Review: translations, stretches, and mixed problems.

Review: translations, stretches, and mixed problems.

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Pre-Cal 40S March 1, 2009 Presentation Transcript

  • 1. Looking Back At The Last Week I am looking forward, thinking back times by flickr user HAMED MASOUMI
  • 2. FUNCTIONS FUNCTIONS odd even
  • 3. Stretches and Compressions: The role of parameter a: Examples a > 1 the graph of ƒ(x) is stretched vertically. 0 < |a| < 1 the graph of ƒ(x) is compressed vertically. - the y-coordinates of ƒ are multiplied by a. The role of parameter b: b > 1 the graph of ƒ(x) is compressed horizontally. (Everything quot;speeds upquot;) 0<|b|<1 the graph of ƒ(x) is stretched horizontally. (Everything quot;slows downquot;) - the x-coordinates are multiplied by .
  • 4. Putting it all together ... Try these examples ... y = ƒ(x) REMEMBER: stretches before translations Don't Look Behind Here Really! Are you sure you want to do this?
  • 5. Practice what you've learned ... The coordinates of a point, A, on the graph of y = ƒ(x) are (-2, -3). What are the coordinates of it's image on each of the following graphs: The image of point B after each transformation shown above is given below as point C(n). Find the original coordinates of B. C3 (5, -4) C4 (-1, 6) C2 (-3, 7) C1 (2, 3) C5 (-4, -2)
  • 6. Consider the equation below. Which transformation do you think should be applied first? second? third? fourth?