Open the “Multiplicity” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.

(a) Use the slider to set a to 1, b to 2, and c to 1. What are the zeros of f?

(b) (i) Leave a set to 1, b to 2, and c to 1. Note the behavior of the graph of the polynomial function near each zero.

(ii) Leave the slider for b at 2 and c at 1. Now use the slider to change a from 1 to 2 to 3 to 4. As you do this, notice the behavior of the graph of the polynomial function at x = 3.

(iii) Set the slider for a to 1 and c to 1. Now use the slider to change b from 1 to 2 to 3 to 4. As you do this, notice the behavior of the graph of the polynomial function at x = −1.

(iv) Based on the results from parts (i)–(iii), if the zero of a polynomial function is of even multiplicity, the graph of the function will______ (cross/touch/avoid) the x -axis at the zero. If the zero of a polynomial function is of odd multiplicity, the graph of the function will________ (cross/touch/avoid) the x -axis at the zero.

(c) Use the slider to set a to 1 and b to 2. Use the slider to change c from − 2 to − 1 to 1 to 2. Note the behavior of the graph near each x -intercept. True or False The value of c affects the behavior of the graph near each x -intercept.