2.2

1. 2.2 Polynomial Functions of Higher Degree

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about • How to use transformations to sketch graphs of Polynomial Functions • How to use the “Leading Coefficient Test” to determine End Behavior of Polynomial Functions • How to find and use Zeros of Polynomial Functions • How to use the Intermediate Value Theorem to locate zeros • … and why These topics are important in modeling various aspects of nature and can be used to provide approximations to more complicated functions.

5. Example Graphing Transformations of Monomial Functions

6. Example Graphing Transformations of Monomial Functions

7. Cubic Functions

8. Quartic Function

9. Local Extrema and Zeros of Polynomial Functions A polynomial function of degree n has at most n – 1 local extrema and at most n zeros.

12. Example Applying Polynomial Theory

13. Example Applying Polynomial Theory

15. Example Finding the Zeros of a Polynomial Function

16. Example Finding the Zeros of a Polynomial Function

19. Example Sketching the Graph of a Factored Polynomial

20. Example Sketching the Graph of a Factored Polynomial

21. Intermediate Value Theorem If a and b are real numbers with a < b and if f is continuous on the interval [a,b], then f takes on every value between f(a) and f(b). In other words, if y0 is between f(a) and f(b), then y0=f(c) for some number c in [a,b].