1 / 16

Section 3.2 Polynomial Functions and Their Graphs

Chapter 3 – Polynomial and Rational Functions. Section 3.2 Polynomial Functions and Their Graphs. Definition. Example. Find the degree, leading coefficient, leading term, coefficients, and constant terms of the below polynomial function. Definition.

ranger
Download Presentation

Section 3.2 Polynomial Functions and Their Graphs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 3 – Polynomial and Rational Functions Section 3.2 Polynomial Functions and Their Graphs 3.2 - Polynomial Functions and Their Graphs

  2. Definition 3.2 - Polynomial Functions and Their Graphs

  3. Example • Find the degree, leading coefficient, leading term, coefficients, and constant terms of the below polynomial function. 3.2 - Polynomial Functions and Their Graphs

  4. Definition • The graph of a polynomial function is continuous meaning the graph has no breaks or holes. The graph is also smooth and has no corners or cusps (sharp points). 3.2 - Polynomial Functions and Their Graphs

  5. Example • Determine which of the graphs below are continuous. 3.2 - Polynomial Functions and Their Graphs

  6. Definition • The end behavior of a polynomial is a description of what happens as x becomes large in the positive or negative direction. We use the following notation: x→∞ means “x becomes large in the positive direction” x →-∞ means “x becomes large in the negitivedirection” 3.2 - Polynomial Functions and Their Graphs

  7. End Behavior • The end behavior of a polynomial is determined by the degree n and the sign of the leading coefficient an. 3.2 - Polynomial Functions and Their Graphs

  8. End Behavior • The end behavior of a polynomial is determined by the degree n and the sign of the leading coefficient an. 3.2 - Polynomial Functions and Their Graphs

  9. Guidelines for Graphing 3.2 - Polynomial Functions and Their Graphs

  10. Example – pg. 244 #19 • Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits proper end behavior. 3.2 - Polynomial Functions and Their Graphs

  11. Definition • If c is a zero of a polynomial P, and the corresponding factor x – c occurs exactly m times in the factorization of P, then we say that c is a zero of multiplicity m. • Multiplicity helps determine the shape of a graph. 3.2 - Polynomial Functions and Their Graphs

  12. Shape of a Graph near Zero 3.2 - Polynomial Functions and Their Graphs

  13. Definitions • If the point (a, f (a)) is the highest point on the graph of f within some viewing rectangle, then f (a) is a local maximum. • If the point (a, f (a)) is the lowest point on the graph of f within some viewing rectangle, then f (a) is a local minimum. • The local minimum and maximum on a graph of a function are called its local extrema. 3.2 - Polynomial Functions and Their Graphs

  14. Local Extrema 3.2 - Polynomial Functions and Their Graphs

  15. Local Extrema of Polynomials • If P(x) = anxn + an-1xn-1 + … + a1x + a0 is a polynomial of degree n, then the graph of P has at most n – 1 local extrema. 3.2 - Polynomial Functions and Their Graphs

  16. Example • Graph the polynomial below and identify all extrema, solutions, multiplicity, and end behavior. 3.2 - Polynomial Functions and Their Graphs

More Related