graphing reciprocal functions
DESCRIPTION
Graphing Reciprocal Functions. 1. Parent Function & Definitions. 2. Transformations. 3. Practice Problems. Definitions. Asymptote The line the graph approaches, but does not touch Horizontal (k) Vertical (h) Parent Function. Each part of the graph is called a branch. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/1.jpg)
Graphing Reciprocal Functions
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11 Parent Function & Definitions
Transformations
Practice Problems
![Page 2: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/2.jpg)
Definitions
Asymptote The line the graph approaches, but does
not touch Horizontal (k) Vertical (h)
Parent Function
2
xy
1
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3
xy
1
Each part of the graph is called a branch.
The x-axis is the horizontal asymptote.
The y-axis is the vertical asymptote.
![Page 4: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/4.jpg)
The general form of a family member is
with a single real number h missing from its domain.
![Page 5: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/5.jpg)
![Page 6: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/6.jpg)
Translations of
Stretch (|a| > 1)
Shrink (0 < |a| < 1)
Reflection (a < 0) in x-axis
Translation (horizontal by h; vertical by k) withvertical asymptote x = h,horizontal asymptote y = k
![Page 7: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/7.jpg)
Solution: Change the equation to xy = 6 and make a table.
![Page 8: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/8.jpg)
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x- and y-axes are the asymptotes.
The graph is the reflection of y = 12/x over the x-axis.
The graph is a stretch of y = 1/x by a factor of 12.
![Page 10: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/10.jpg)
x- and y-axes are the asymptotes.
The graph is the reflection of y = 4/x over the x-axis.
The graph is a stretch of y = 1/x by a factor of 4.
![Page 11: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/11.jpg)
The asymptotes are x = -7 and y = -3.
![Page 12: Graphing Reciprocal Functions](https://reader034.vdocuments.mx/reader034/viewer/2022052117/56812cdd550346895d91a437/html5/thumbnails/12.jpg)
that has asymptotes at x = -2 and y = 3 and then graph.
h = -2 and k = 3.Solution:
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that is 4 units to the left and 5 units up.
Solution: h = -4 and k = 5.