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Graphing Reciprocal Functions

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.

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Graphing Reciprocal Functions

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

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

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

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

  5. Translations of 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

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

  7. 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.

  8. 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.

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

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

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

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