Graphing Reciprocal Functions

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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.

The general form of a family member is

with a single real number h missing from its domain.

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

Solution: Change the equation to xy = 6 and make a table.

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.

The asymptotes are x = -7 and y = -3.

that has asymptotes at x = -2 and y = 3 and then graph.

h = -2 and k = 3.Solution:

that is 4 units to the left and 5 units up.

Solution: h = -4 and k = 5.