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Stretches ...
                 and some
                 reflections.




Ballet stretch
Pre-Cal 40S Slides February 28, 2008
Pre-Cal 40S Slides February 28, 2008
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.
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 ...
Pre-Cal 40S Slides February 28, 2008
Pre-Cal 40S Slides February 28, 2008
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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Pre-Cal 40S Slides February 28, 2008

  • 1. Stretches ... and some reflections. Ballet stretch
  • 4. 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.
  • 5. 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 ...
  • 8. 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 .