Fields of Functions 3 Copyright © 2026 Pearson Education, Inc. Fields of Functions (50 – 60 minutes) Learning Objective(s): ● Students will evaluate functions given in function notation for inputs in the domain. ● Students will identify and analyze key features of linear and quadratic functions. ● Students will determine whether a linear or quadratic function better models a given real-world situation. ● Students will apply function analysis to model crop yields under different environmental conditions. Material needed: ● Student pages: Fields of Functions ● Calculator ● Graphing software (optional) ● Coloring pencils (optional) Lesson Procedure: Warm–Up 10 minutes Prompt: In farming, crop growth varies over time. Sometimes growth can be steady and predictable; other times it increases rapidly before leveling off or declining. What mathematical functions best model these patterns, and how might their features enhance our understanding of crop development? Discuss: linear function, quadratic function, increasing, decreasing, end behavior Guided Instruction 15 minutes Present: scenario for Fields of Functions. Example: A farmer tracks how two crops grow over time. Crop A is modeled by f(t) = 3t + 5. Crop B is modeled by g(t) = –t2 + 6t; t is time in weeks; f(t) and g(t) represent yield in kg. Compare f(t) and g(t). What do you notice? f(t) is linear; for each week, the crop yield increases by 3 kg; g(t) is quadratic, increasing rapidly and then decreasing after reaching a certain point. Review: key terms – domain, range, end behavior, Intercepts domain: all possible input values range: all possible output values end behavior: how a function's output behaves as the input approaches positive or negative infinity intercept: the point where a line or curve crosses the x- or y-axis Independent Practice 20 minutes Distribute: student activity Fields of Functions Allow students to work individually or in pairs. Closure 10–15 minutes Review Answers: 1. a. f(0) = 2; b. f(2) = 5.6; c. f(4) = 9.2; d. f(6) = 12.8; e. f(8) = 16.4; . f. Sample answer: Every 2 weeks, the yield increases by 3.6 kg. 2. a. g(0) = 2; b. g(2) = 8; c. g(4) = 10; d. g(6) = 8; e. g(8) = 2; f. Sample answer: Crop B starts to decrease by t = 6. 3. domain: t ≥ 0 4. range: f(t) greater than 2; g(t) from 2 to 10 5. See graph. 6. f(t): intercept at (0, 2); increases for all t ≥ 0 without bound 7. g(t): intercept at (0, 2); increases on [0, 4], decreases after 4 Discuss: Why is it important to select the correct model when planning agricultural decisions in different parts of the world?
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