1. Symmetry and Coordinate Graphs Symmetry and Coordinate Graphs Section 3-1 How do we determine symmetry using algebra? How do we classify functions as even or odd? Essential Questions:

2. Possible types of symmetry are: with respect to the x-axis with respect to the y-axis with respect to the origin with respect to the line y = x with respect to the line y = -x

3. Table of Symmetric Relationships Symmetry with respect to: What do we do?Example x-axis y-axis origin y = x y = -x

4. x-axis keep x the same but negate y What we do What we do: (1, 2) (1, -2) Equals original function

5. y-axis keep y the same but negate x What we do What we do: (-1, 2) (1, 2) Equals original function

6. origin negate x AND negate y What we do What we do: (-1, 3) (1, -3) Equals original function

7. y = x interchange (swap) x and y What we do What we do: Equals original function (2, 3) (3, 2)

8. y = -x interchange AND negate x and y What we do What we do: Equals original function (-3, -2) (2, 3)

9. Example 1 x-axis y-axis origin y = x y = -x No Yes Determine the types of symmetry for the graph of xy = -2

10. Example 2 x-axis y-axis origin y = x y = -x yes no Determine the types of symmetry for the graph of

11. Classifying Functions as Even or Odd EVEN functions are symmetric with respect to the y-axis ODD functions are symmetric with respect to the origin