# Zeros of multiplicity

- Author:
- Jon Hasenbank

- Topic:
- Algebra

Turn on the green function and slider and observe how the graph behaves near x = 1.
Turn on the blue function and slider and observe how the graph behaviors near x = 1.

1. What do you notice?
2. How is the behavior of a function near one of its zeros related to the multiplicity of that zero?
3. Compare and contrast the results when the multiplicity is even (green functions) or odd (blue function)?