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CHAPTER_ppt_8_3 - Beginning and Intermediate Algebra 4ed 5...

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§ 8.3 Graphing Piecewise- Defined Functions and Shifting and Reflecting Graphs of Functions
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Graph each “piece” separately. Graph 3 1 if 0 ( ) . 3 if 0 x x f x x x - = + Graphing Piecewise-Defined Functions Continued. x f ( x ) = 3 x – 1 0 – 1 (closed circle) –1 – 4 –2 – 7 x f ( x ) = x + 3 1 4 2 5 3 6 Values 0. Values > 0. Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Graphing Piecewise-Defined Functions x y x f ( x ) = x + 3 1 4 2 5 3 6 x f ( x ) = 3 x – 1 0 – 1 (closed circle) –1 – 4 –2 – 7 (0, –1) (–1, 4) (–2, 7) Open circle (0, 3) (3, 6) Example continued:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Vertical and Horizontal Shifting Vertical Shifts (Upward or Downward) Let k be a Positive Number Graph of Same As Moved g ( x ) = f ( x ) + k f ( x ) k units upward g ( x ) = f ( x ) - k f ( x ) k units downward Horizontal Shifts (To the Left or Right) Let h be a Positive Number Graph of Same As Moved g ( x ) = f ( x - h ) f ( x ) h units to the right g ( x ) = f ( x + h ) f ( x ) h units to the left
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Martin-Gay,
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Unformatted text preview: Beginning and Intermediate Algebra, 4ed 5 2 Graph ( ) 3. f x x =-x y 5 5-5-5 Begin with the graph of f ( x ) = x 2 . Shift the original graph downward 3 units. (0, –3) Vertical and Horizontal Shifting Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 Graph ( ) 2 . f x x = + Begin with the graph of f ( x ) = | x| . Shift the original graph to the left 2 units. (0, –2) x y 5 5-5-5 Vertical and Horizontal Shifting Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 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. Martin-Gay, Beginning and Intermediate Algebra, 4ed 8 Reflect the original graph about the x-axis . Reflections of Graphs Graph ( ) . f x x = -Begin with the graph of ( ) . f x x = x y 5 5-5-5 (4, –2) (4, 2) Example:...
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