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# 6.4 Reciprocal Functions (Lines)

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### 6.4 Reciprocal Functions (Lines)

1. 1. 6.4 Reciprocal Functions (Linear Functions)1May 06, 20136 6.4  Reciprocal FunctionsReview:ReciprocalsWhatisthereciprocalof...5‐1/23/4
2. 2. 6.4 Reciprocal Functions (Linear Functions)2May 06, 20136 6.4  Reciprocal FunctionsReview:ReciprocalsTherefore,thereciprocalofafunction f(x)is
3. 3. 6.4 Reciprocal Functions (Linear Functions)3May 06, 2013
4. 4. 6.4 Reciprocal Functions (Linear Functions)4May 06, 20136.4Letscomparetwographs, f(x)and 1/f(x)f(x)=xg(x)=1/f(x)=1/x
5. 5. 6.4 Reciprocal Functions (Linear Functions)5May 06, 2013
6. 6. 6.4 Reciprocal Functions (Linear Functions)6May 06, 20136.4Letscomparetwographs, f(x)and 1/f(x)Thegraphhastwodistinctpieces(called branches).Thesebranchesarelocatedoneithersideofthe vertical and horizontalasymptotes.verticalasymptotehorizontalasymptote
7. 7. 6.4 Reciprocal Functions (Linear Functions)7May 06, 20136.4The horizontalasymptotedescribesthebehaviourofthegraphforverylargepositiveandnegativevaluesofx.Theline y=b isahorizontalasymptoteifthevaluesofthefunctionapproach bforverylargepositiveornegativevaluesofxThe verticalasymptoteoccursatthenon‐permissiblevaluesofthefunction.Theline x=a isaverticalasymptoteifthecurveapproachesthelinemoreandmorecloselyasxapproaches a,andthevaluesofthefunctionincreaseordecreasewithoutboundasxapproaches a
8. 8. 6.4 Reciprocal Functions (Linear Functions)8May 06, 20136.4f(x)=xg(x)=1/f(x)=1/xLetscomparetwographs, f(x)and 1/f(x)Characteristic y=x y=1/xDomainRangeEndBehaviourBehaviouratx=0invariantpoints
9. 9. 6.4 Reciprocal Functions (Linear Functions)9May 06, 20136.4Graph the Reciprocal of a Linear FunctionConsider 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.
10. 10. 6.4 Reciprocal Functions (Linear Functions)10May 06, 2013
11. 11. 6.4 Reciprocal Functions (Linear Functions)11May 06, 2013