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Algebra IIA Unit VI: Properties and Attributes of Functions • Foundational Material o Prior study of various functions, graphs and equations o Perform algebraic operations on various expressions • • o Perform transformations of various functions o Model real world applications with functions Goal Model real-world data with functions Perform operations on functions Why? To further build a foundation for higher level mathematics To solve problems in other classes such as chemistry, physics, and biology Make predictions by modeling data involving time, money, speed, sports, travel, etc. • Key Vocabulary o Composition of functions Lesson I: Operations with Functions • • • • Add, subtract, multiply and divide functions. Write and evaluate composition functions. Combine standard function types using arithmetic operations. (CC.9-12.F.BF.1b) Compose functions. (CC.9-12.F.BF.1c) Rules: (f + g)(x) = ______________________________________________________________ (f – g)(x) = ______________________________________________________________ (fg)(x) = ________________________________________________________________ (f/g)(x) = ________________________________________________________________ (fog)(x) = ________________________________________________________________ Operations with Functions () () Find and simplify the following given that f x = 2x 2 + 4x - 6 and g x = 2x - 2. (f + g)(x) = (fog)(x) = (f – g)(x) = (fg)(x) = (gof)(x) = sd (f/g)(x) = (fog)(3) = () () Find and simplify the following given that f x = 5x - 6 and g x = x 2 - 5x + 6. (f + g)(x) = (f – g)(x) = (fog)(x) = sd (fg)(x) = (f/g)(x) = (gof)(x) = () (gof)(2) = () Find and simplify the following given that f x = 3x - 4 and g x = x + 2. (f + g)(x) = (f – g)(x) = (fog)(x) = sd (fg)(x) = (f/g)(x) = (gof)(x) = (gof)(2) = You try: Evaluate given that f(x) = x2 – 1 and g(x) = 2x + 3 1) f(2) 2) f(-3) 3) g(4) 4) g(-1) Examples: Find a rule for the following given the functions below… You try: f(x) = 4x2 + 3x – 1 g(x) = 6x + 2 h(x) = 6x2 – x – 12 1) (f + g)(x) 2) (f – g)(x) 3) (hj)(x) 4) h x j j(x) = 2x – 3 Evaluate: 5) (f + j)(2) 6) (h – g)(1) 7) (g j)(0) 8) g 1 h Given f(x) = 2x and g(x) = 7 – x, find the following: 9) f(g(4)) 10) g(f(4)) Assignment: Page 446, 15-32, 39-42