# Multiplicity and Turning Points

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