CHAPTER 2. Polynomial Functions

Transcription

1 CHAPTER Polynomial Functions.1 Graphing Polynomial Functions...9. Dividing Polynomials...5. Factoring Polynomials...1. Solving Polynomial Equations The Fundamental Theorem of Algebra...5. Transformations of Polynomial Functions Analyzing Graphs of Polynomial Functions Modeling with Polynomial Functions Performing Function Operations Inverse of a Function

2 Name Date Chapter Maintaining Mathematical Proficiency Simplify the epression r 5 + 7r r t 9 + t 8t. ( a + ) 5. + ( 5) +. y ( y ) ( h 7) 7( 10 h) ( ) + ( ) Solve the equation by factoring = = = = 1. = = = 17. = = 8

3 Name Date.1 Graphing Polynomial Functions For use with Eploration.1 Essential Question What are some common characteristics of the graphs of cubic and quartic polynomial functions? 1 EXPLORATION: Identifying Graphs of Polynomial Functions Go to BigIdeasMath.com for an interactive tool to investigate this eploration. Work with a partner. Match each polynomial function with its graph. Eplain your reasoning. Use a graphing calculator to verify your answers. a. f ( ) = b. f ( ) = + c. f( ) = + 1 d. f ( ) = e. f ( ) = f. f ( ) = A. B. C. D. E. F. 9

4 Name Date.1 Graphing Polynomial Functions (continued) EXPLORATION: Identifying -Intercepts of Polynomial Graphs Work with a partner. Each of the polynomial graphs in Eploration 1 has -intercept(s) of 1, 0, or 1. Identify the -intercept(s) of each graph. Eplain how you can verify your answers. Communicate Your Answer. What are some common characteristics of the graphs of cubic and quartic polynomial functions?. Determine whether each statement is true or false. Justify your answer. a. When the graph of a cubic polynomial function rises to the left, it falls to the right. b. When the graph of a quartic polynomial function falls to the left, it rises to the right. 0

5 Name Date.1 Notetaking with Vocabulary For use after Lesson.1 In your own words, write the meaning of each vocabulary term. polynomial polynomial function end behavior Core Concepts End Behavior of Polynomial Functions Degree: odd Leading coefficient: positive Degree: odd Leading coefficient: negative y f() + as + f() + as y f() as f() as + Degree: even Leading coefficient: positive Degree: even Leading coefficient: negative f() + as y f() + as + y f() as f() as + Notes: 1

6 Name Date.1 Notetaking with Vocabulary (continued) Practice A Etra Practice In Eercises 1, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. 1. f( ) = ( ) m = p = +. g( ) = ( ) In Eercises 5 and, evaluate the function for the given value of. 5. h ( ) = + ; =. ( ) g = + 5; = In Eercises 7 and 8, describe the end behavior of the graph of the function. f = f( ) = ( ) 9. Describe the degree and leading coefficient of the polynomial function using the graph. y

7 Name Date.1 Notetaking with Vocabulary (continued) In Eercises 10 and 11, graph the polynomial function p( ) = ( ) g = + 1. Sketch a graph of the polynomial function f if f is increasing when < 1and 0 < < 1, f is decreasing when 1 < < 0and > 1, and f ( ) < 0for all real numbers. Describe the degree and leading coefficient of the function f. 1. The number of students S (in thousands) who graduate in four years from a university can be modeled by the function St () = 1 t + t +, where t is the number of years since 010. a. Use a graphing calculator to graph the function for the interval 0 t 5. Describe the behavior of the graph on this interval. b. What is the average rate of change in the number of four-year graduates from 010 to 015? c. Do you think this model can be used for years before 010 or after 015? Eplain your reasoning.

8 Name Date Practice.1 BPractice B In Eercises 1, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. 1. h ( ) = ( ) f = g ( ) = 1 +. f( ) In Eercises 5 7, evaluate the function for the given value of. f = ; = ( ) g = ; =. ( ) 1 h = ; = 7. ( ) 1 = In Eercises 8 and 9, describe the end behavior of the graph of the function. g = ( ) h = ( ) 5 In Eercises 10 1, graph the polynomial function. 10. q ( ) = h ( ) = k ( ) = + 1. ( ) f = In Eercises 1 and 15, sketch a graph of the polynomial function f having the given characteristics. Use the graph to describe the degree and leading coefficient of the function f. 1. f is increasing when < 1; f is decreasing when > 1. ( ) 0 f > when 1 ; < < ( ) 0 f < when < 1 and >. 15. f is increasing when < 1.1 and >.; f is decreasing when 1.1 < <.. ( ) 0 f > when < < 0 and ; 0 < <. f < when < and > ( ) 0 1. The function ht () =.9t + 8.t +. models the height h of a high pop-up hit by a baseball player after t seconds. Use a graphing calculator to graph the function. State an appropriate window to view the maimum height of the ball and when the ball hits the ground.