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

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

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

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

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

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

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
x-axis
y-axis
origin
y = x
y = -x No
Yes

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

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