Section 4.3 Reflecting Graphs; Symmetry

1. Section 4.3Reflecting Graphs; Symmetry

2. Graph: y = -(x2 – 1) Graph: y = x2 – 1

3. Graph: y = -|x2 – 1| Graph: y = |x2 – 1|

4. Graph: y = (-x + 2)2 Graph: y = (x + 2)2

5. Graph: x = y2 Graph: y = x2

6. Graph: y = x3

7. Tests for Symmetry: • x-axis symmetry: (x, y) and (x, -y) are both on the graph • Test: -leave x -plug in –y for y -see if the equations are equal • y-axis symmetry: (x, y) and (-x, y) are both on the graph • Test: -leave y -plug in –x for x -see if the equations are equal

8. …Tests for Symmetry: • y = x symmetry: (x, y) and (y, x) are both on the graph • Test: -switch x andy -see if the equations are equal • origin symmetry: (x, y) and (-x, -y) are both on the graph • Test: -plug in –x for x -plug in –y for y -see if the equations are equal

9. Ex. 1: Let f(x) = 2x – 3. Sketch each graph: a. y = -f(x)

10. Ex. 1: Let f(x) = 2x – 3. Sketch each graph: b. y = |f(x)|

11. Ex. 1: Let f(x) = 2x – 3. Sketch each graph: c. y = f(-x)

12. Ex. 2: Test x2 = y2 – 1 for each type of symmetry:

13. Homework :pg. 135 1-4pg. 136 1-5, 8, 10, 11, 15, 16, 31