Polynomial Function from Graph Worksheet

Polynomial Function from Graph Worksheet

Carefully analyze each graph of a polynomial function. Determine the roots, their multiplicities, and the end behavior. Then, write the possible equation for the polynomial function in factored form.

1. Consider the graph of the polynomial function below:

Identify the roots and their multiplicities. Describe the end behavior. Write a possible equation for the polynomial function in factored form.

2. If a polynomial graph touches the x-axis and turns around at a root, the multiplicity of that root is   (even/odd). If it crosses the x-axis at a root, the multiplicity is   (even/odd).

3. Sketch a graph of a polynomial function that has roots at x = -3 (multiplicity 1), x = 0 (multiplicity 2), and x = 2 (multiplicity 1). Describe its end behavior.

4. A polynomial function with an odd degree must have at least one real root.

5. A polynomial function has roots at x = -1, x = 1, and x = 3. The graph crosses the x-axis at x = -1 and x = 3, but touches and turns at x = 1. The graph rises to the left and falls to the right. Write a possible equation for this polynomial function.