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§ 8.3

Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions. § 8.3. Graph. Graphing Piecewise-Defined Functions. Example:. Graph each “piece” separately. Values  0. Values > 0. Continued. y. (3, 6). Open circle. (0, 3). x. (0, –1). (–1, 4). (–2, 7).

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§ 8.3

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  1. Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions § 8.3

  2. Graph Graphing Piecewise-Defined Functions Example: Graph each “piece” separately. Values  0. Values > 0. Continued.

  3. y (3, 6) Open circle (0, 3) x (0, –1) (–1, 4) (–2, 7) Graphing Piecewise-Defined Functions Example continued:

  4. Vertical and Horizontal Shifting Vertical Shifts (Upward or Downward) Let k be a Positive Number Horizontal Shifts (To the Left or Right) Let h be a Positive Number

  5. y 5 x 5 5 (0, –3) 5 Vertical and Horizontal Shifting Example: Begin with the graph of f(x) = x2. Shift the original graph downward 3 units.

  6. y 5 x 5 5 5 (0, –2) Vertical and Horizontal Shifting Example: Begin with the graph of f(x) = |x|. Shift the original graph to the left 2 units.

  7. Reflections of Graphs Reflection about the x-axis The graph of g(x) = – f(x) is the graph of f(x) reflected about the x-axis.

  8. y 5 (4, 2) x 5 5 5 (4, –2) Reflections of Graphs Example: Reflect the original graph about the x-axis.

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