Zeros of multiplicity

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)?