# Multiplicity and Turning Points

- Author:
- Carlos B. Vizcaino

On the screen you will see the graph of where a={1, 2, 3}, b={1, 2, 3}, and c={1, 2, 3, 4}

**1.**Grab the slider for the exponent*a*and move it from 1 to 2 to 3. What happens to the graph as the value of*a*changes? In particular, describe the behavior of the graph around the zero -2.**2.**On the same graph, grab the slider for the exponent*a*and move it to 1. Grab the slider for the exponent*b*and move it from 1 to 2 to 3. What happens to the graph as the value of*b*changes? In particular, describe the behavior of the graph around the zero 0.**3.**On the same graph, grab the slider for the exponent*b*and move it to 1. Grab the slider for the exponent*c*and move it from 1 to 2 to 3 to 4.What happens to the graph as the value of*c*changes? In particular, describe the behavior of the graph around the zero 2.**4.**Experiment with the graph by adjusting*a, b*, and*c*. Based on your experiences conjecture the role the exponent plays in the behavior of the graph around each zero of the function. -2