1. Warm-Up:

2. 2.2 – Polynomial Functions
Objective: graph polynomial functions & model real-world data with polynomial functions.

3. Polynomial Graphs:

4. Example 1:
Describe the transformation of the graph, then give domain, range, intercepts, end behavior, continuity, & increasing and/or decreasing intervals. a. f (x) = (x – 3)5 b. f (x) = x 6 – 1

6. Example 2:
Without a calculator, describe the end behavior of the graph using limits. Explain your reasoning using the leading term test.
a. f (x) = 3x 4 – x 3 + x 2 + x – 1
b. f (x) = –3x 2 – 2x 5 – x 3

7. Turning Points: where the graph of a function changes from increasing to decreasing and vice versa.
How are zeros related to turning points???

9. Example 3:
State the number of possible real zeros and turning points of f (x) = x 3 + 5x 2 + 4x. Then determine all of the real zeros by factoring.

10. Example 4:
State the number of possible real zeros and turning points. Then determine all of the real zeros by factoring. a. g (x) = x 5 – 5x 3 – 6x b. h (x) = x 4 + 5x 3 + 6x 2

12. Example 5:
For f (x) = x(3x + 1)(x – 2) 2: A. Apply the leading-term test. B. Determine the zeros and state the multiplicity of any repeated zeros.

13. Example 5:
C. Sketch the graph (without a calculator).

14. Example 6: A. 0, –2 (multiplicity 2), (multiplicity 3)
Determine the zeros and state the multiplicity of any repeated zeros for f (x) = 3x(x + 2)2(2x – 1)3. Then sketch the graph.
A. 0, –2 (multiplicity 2), (multiplicity 3)
B. 2 (multiplicity 2), – (multiplicity 3)
C. 4 (multiplicity 2), (multiplicity 3)
D. –2 (multiplicity 2), (multiplicity 3)