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.  Line of Reflection  acts like a mirror  located halfway between a point and its reflection  Reflecting Across: 1.x-axis 2.y-axis 3.line y = x REFLECTING GRAPHS

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.

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.

8. The graph of f(x) = x 2 + 2 is shown. Y = X REFLECTION 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. EXAMPLE SKETCH GRAPH ACROSS Y = X

10. ABSOLUTE VALUE REFLECTION The absolute value reflection of f(x) = x 2 – 5 is shown. Describe a rule for absolute value reflections.

12. IDENTIFY WHICH TYPE(S) OF REFLECTION CAN BE SEEN IN EACH GRAPH.

13. ASSIGNMENT Textbook pg. 136 #1-4

14. 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 symmetryO is the point of symmetry SYMMETRY

15. EQUATIONS FOR SYMMETRY

16. EXAMPLE FIND A LINE OF SYMMETRY

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 p. 134 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 y-axis.

19. p. 134 SPECIAL TESTS FOR THE SYMMETRY OF A GRAPH Both points (x, y) and (y, x) on the graph You only need to graph one branch. The other branch can be obtained by reflecting the graphed branch about the line y = x.

20. p. 134 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 origin.

21. Reflect x-axis Reflect y-axis Above x-axis c whole number – stretch c fraction – shrink (vertically) c whole number – shrink c fraction – stretch (horizontally) Shift up or down Shift right or left TRANSLATIONS – SUMMARY

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