1. Graphing Reciprocal Functions1
Parent Function & Definitions 2
Transformations 3
Practice Problems

2. Definitions Parent Function Asymptote
The line the graph approaches, but does not touch
Horizontal (k)
Vertical (h)
Parent Function

3. The x-axis is the horizontal asymptote.
Each part of the graph is called a branch.
The x-axis is the horizontal asymptote.
The y-axis is the vertical asymptote.

4. with a single real number h missing from its domain.
The general form of a family member is
with a single real number h missing from its domain.

6. Translations of Shrink (0 < |a| < 1)
Stretch (|a| > 1)
Shrink (0 < |a| < 1)
Reflection (a < 0) in x-axis
Translation (horizontal by h; vertical by k) with
vertical asymptote x = h,
horizontal asymptote y = k

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

9. The graph is a stretch of y = 1/x by a factor of 12.
The graph is the reflection of y = 12/x over the x-axis.
x- and y-axes are the asymptotes.

10. 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 graph is the reflection of y = 4/x over the x-axis.
x- and y-axes are the asymptotes.

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

12. that has asymptotes at x = -2 and y = 3 and then graph.
Solution:
h = -2 and k = 3.

13. that is 4 units to the left and 5 units up.
Solution:
h = -4 and k = 5.