6.4 reciprocal functions line F2012

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6.4 reciprocal functions line F2012

  1. 1. 4 Reciprocal Functions (Line) December 10, 2012 Chapter  6 6.4  Reciprocal Functions Review:Reciprocals Whatisthereciprocalof... 5 ‐1/2 3/46 Absolute Values and Reciprocal Functions
  2. 2. 4 Reciprocal Functions (Line) December 10, 2012 Chapter  6 6.4  Reciprocal Functions Review:Reciprocals Therefore,thereciprocalofafunction f(x) is6 Absolute Values and Reciprocal Functions
  3. 3. 4 Reciprocal Functions (Line) December 10, 2012 6.4 Letscomparetwographs, f(x)and 1/f(x) f(x)=x g(x)=1/f(x)=1/x6 Absolute Values and Reciprocal Functions
  4. 4. 4 Reciprocal Functions (Line) December 10, 2012 6.4 Letscomparetwographs, f(x)and 1/f(x) Thegraphhastwodistinctpieces(called branches).Thesebranches arelocatedoneithersideofthe vertical and horizontalasymptotes. verticalasymptote horizontalasymptote6 Absolute Values and Reciprocal Functions
  5. 5. 4 Reciprocal Functions (Line) December 10, 2012 6.4 The horizontalasymptote describesthebehaviourofthegraphforverylarge positiveandnegativevaluesofx.Theline y=b isahorizontalasymptoteifthevalues ofthefunctionapproach bforverylargepositiveornegativevaluesofx The verticalasymptote occursatthenon‐permissiblevaluesofthefunction.The line x=a isaverticalasymptoteifthecurveapproachesthelinemoreandmore closelyasxapproaches a,andthevaluesofthefunctionincreaseordecrease withoutboundasxapproaches a6 Absolute Values and Reciprocal Functions
  6. 6. 4 Reciprocal Functions (Line) December 10, 2012 6.4 Letscomparetwographs, f(x)and 1/f(x) f(x)=x g(x)=1/f(x)=1/x Characteristic y=x y=1/x Domain Range EndBehaviour Behaviouratx=0 invariant points6 Absolute Values and Reciprocal Functions
  7. 7. 4 Reciprocal Functions (Line) December 10, 2012 6.4 Graph the Reciprocal of a Linear Function Consider f (x) = 2x + 5. a) Determine its reciprocal function             . b) Determine the equation of the vertical asymptote of the reciprocal function. c) Graph the function y = f (x) and its reciprocal function             .     Describe a strategy that could be used to sketch the graph of a     reciprocal function.6 Absolute Values and Reciprocal Functions
  8. 8. 4 Reciprocal Functions (Line) December 10, 20126 Absolute Values and Reciprocal Functions

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