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 functions. ● 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: function, linear, constant, increasing, decreasing Guided Instruction 15 minutes Present: scenario for Fields of Functions. Example: A farmer tracks weekly growth in kilograms for a crop modeled by f(t) = 3t + 5. What does f(t) mean in this context? f(t) represents the crop’s yield on kilograms at week t. What does f(4) tell us? f(4) = 3(4) + 5 = 17; so, after 4 weeks, the yield is 17 kg. Review: key terms – function notation, input, output, domain, range function notation: a way to represent relationships between variables, using the form f(x) = y input: value or set of values that are entered into a function output: the result produced by a calculation when a specific input is provided domain: all possible input values range: all possible output values 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. After 3 weeks, Crop A yields 7.4 kg. 4. week 4 5. See graph. 6. domain: t ≥ 0 7. range: f(t) greater than 2; g(t) from 2 to 10 8. f(t) models steady, constant growth ideal for stable conditions. g(t) models growth that accelerates then slows or declines, representing more variable conditions. Discuss: Why is it useful for global farmers or business planners to know how to evaluate these functions? How does this information support better planning for harvesting, shipping, or pricing?
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