Pre-Cal 40S Slides February 28, 2008

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Stretches and reflections.

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Pre-Cal 40S Slides February 28, 2008

  1. 1. Stretches ... and some reflections. Ballet stretch
  2. 2. Translations y = ƒ(x - a) + b The role of parameter a: Examples a > 0 the graph shifts right a units. - the x-coordinates are increased a units. a < 0 the graph shifts left a units. - the x-coordinates are decreased a units. WARNING: watch the sign of a The role of parameter b: b > 0 the graph shifts up b units. - the y-coordinates are increased b units. b < 0 the graph shifts down b units. - the y-coordinates are decreased b units.
  3. 3. Stretches ... (and a wee bit about reflections) Let's start with a circle ... Let's look at some graphs ... We'll head over to fooplot.com ...
  4. 4. Stretches and Compressions: DICTIONARY The role of parameter a: a > 1 the graph of ƒ(x) is stretched vertically. Examples 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 .

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