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Graphing Reciprocal Functions
33
22
11 Parent Function & Definitions
Transformations
Practice Problems
Definitions
Asymptote The line the graph approaches, but does
not touch Horizontal (k) Vertical (h)
Parent Function
2
xy
1
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.
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
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.
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.