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4.3 Reflecting Graphs & Symmetry

4.3 Reflecting Graphs & Symmetry. Learning Objectives. Reflect Graphs Use Symmetry to Sketch Graphs Find Lines of Symmetry “How to use a line symmetry or point symmetry to sketch a graph.”. Reflecting Graphs. Line of Reflection acts like a mirror

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4.3 Reflecting Graphs & Symmetry

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  1. 4.3 Reflecting Graphs & Symmetry

  2. Learning Objectives • Reflect Graphs • Use Symmetry to Sketch Graphs • Find Lines of Symmetry • “How to use a line symmetry or point symmetry to sketch a graph.”

  3. Reflecting Graphs • Line of Reflection • acts like a mirror • located halfway between a point and its reflection • Reflecting Across: • x-axis • y-axis • line y = x

  4. X-Axis Reflection If the red line represents f(x) and the purple line represents –f(x), describe the rule for reflecting across the x axis. • To Graph or a reflecting across the x-axis

  5. ExampleSketch the Graph of

  6. Y-Axis Reflection The red line represents f(x) and the blue line represents f(-x). Describe the rule for reflecting across the y axis. • To Graph or a reflecting across the y-axis

  7. ExampleSketch the Graph of

  8. Y = X Reflection The graph of f(x) = x2 + 2 is shown. To graph the reflection over the line y = x, swap x and y. If a reflection over y = x is found by swapping x and y, what is the notation for this reflection? Find the equation for the reflection of f(x) over y = x line.

  9. ExampleSketch Graph Across y = x • Sketch the graph of • Give an equation for the reflected graph across y = x • Sketch the graph reflected across y = x b)

  10. Absolute Value Reflection To graph find plot all values of above the x axis. Note: is identical to when y > 0 The absolute value reflection of f(x) = x2 – 5 is shown. Describe a rule for absolute value reflections.

  11. ExampleSketch the Graph of

  12. Identify which type(s) of reflection can be seen in each graph.

  13. Assignment Textbook pg. 136 #1-4

  14. Symmetry A line l is called an axis of symmetry of a graph if it is possible to pair the points of the graph in such a way that l is the perpendicular bisector of the segment joining each pair. A point O is called point of symmetry of a graph if it is possible to pair the points of the graph in such a way that O is the midpoint of the segment joining each pair. A point of symmetry signifies a 180 rotation. l is the axis of symmetry Ois the point of symmetry

  15. Equations for Symmetry

  16. ExampleFind a Line of Symmetry • Graph the f • Find the equation for the axis of symmetry. • Graph the axis of symmetry. b)

  17. Special Tests for the Symmetry of a Graph Both points (x, y) and (x, –y) on the graph You only need to graph one branch. The other branch can be obtained by reflecting the graphed branch about the x-axis.

  18. Special Tests for the Symmetry of a Graph Both points (x, y) and (–x, y) on the graph p. 134 You only need to graph one branch. The other branch can be obtained by reflecting the graphed branch about the y-axis.

  19. Special Tests for the Symmetry of a Graph Both points (x, y) and (y, x) on the graph p. 134 You only need to graph one branch. The other branch can be obtained by reflecting the graphed branch about the line y = x.

  20. Special Tests for the Symmetry of a Graph Both points (x, y) and (–x, –y) on the graph p. 134 You only need to graph one branch. The other branch can be obtained by reflecting the graphed branch about the origin.

  21. Translations – Summary

  22. Assignment Textbook pg. 135-137 #2, 7-8, 15-16

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