4.3 Symmetry

1
4.3 Symmetry

1. Which graph is NOT a function?
2. Re-write the graph as two separate functions.
3. Now match each graph with its description.

Absolute Value Cubic Square Root Parabola Constant
Linear
2
Reflection over x-axis
Reflection over y-axis
3
Reflection over line y x
4
Symmetry
5

• Checking for Symmetry algebraically then
  graphically

6

• Checking for Symmetry algebraically then
  graphically

Checking for Symmetry algebraically only
7

• Completing the Graph

Symmetric with respect to the origin
Symmetric with respect to the y-axis
Symmetric with respect to the origin
Symmetric with respect to the x-axis
8

• Point of Symmetry

All odd functions have a point of symmetry
where it is possible to pair the points of the
graph in such a way that the point of symmetry is
the midpoint of the segment joining each pair.
Homework
Pages 136138 1, 47, 9, 12, 14, 15 (a, b), 21a,
23a, 31 (a, b, c), 35, 36
9
Absolute Value

• Unchanged when f(x) 0 and reflected in the
  x-axis when f(x) lt 0.