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Writing Function Rules: Understanding Relationships Through Practical Examples

This resource focuses on developing the skill of writing function rules based on given relationships. Using real-life examples, such as profit calculations in journalism and choir performances, students will learn how to create mathematical expressions that connect independent and dependent variables. The guide emphasizes asking essential questions to establish these relationships and provides exercises to practice writing function rules. By examining situations like profit from ads sold and costs associated with producing goods, learners will gain a clearer understanding of functions in mathematics.

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Writing Function Rules: Understanding Relationships Through Practical Examples

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  1. Writing a Function Rule Unit #6 Day 4

  2. xy 1 2 2 3 3 4 4 5 Writing a Function Rule Ask yourself: “What must I do to turn 1 into 2, 2 into 3, 3 into 4, and so on?” Add 1 to the x value to get the y value. A rule for the function is y = x + 1.

  3. Practice:

  4. Writing a Function From Words • http://www.phschool.com/webcodes10/index.cfm?wcprefix=ate&wcsuffix=0504&area=view&x=-853&y=-349

  5. money earned number of ads sold Relate:    is  25  times   f(n) n Write: = 25 • Writing a Function Rule The journalism class makes $25 per ad sold in the yearbook. If the class sells n ads, how much money will it earn? Write a function rule to describe this relationship. The function rule is f(n) = 25n

  6. total profit tapes sold Relate: is $5.50 times minus cost of tape production f(x) Write: = 5.5 • – 100 x Writing a Function Rule The choir spent $100 producing audio tapes of its last performance and will sell the tapes for $5.50 each. Write a rule to describe the choir’s profit as a function of the number of tapes sold. The function rule is f(x) = 5.5x– 100

  7. Homework • Page 272 • #1-8, 10-13, 17

  8. x ƒ(x) –1 –4 0 –3 1 –2 2 –1 xy –1 –5 0 0 1 5 2 10 b. a. Writing a Function Rule 1. Write a function rule for each table. y = 5x ƒ(x) = x – 3 2. Write a function rule to describe each relationship. a. the total cost T(c) of c pounds of apples at $.82 a pound b. a scale model s of a moth m that is 6 times the actual size of the moth T(c) = 0.82c s(m) = 6m 3. You borrow $60 to buy a bread-making machine. You charge customers $1.50 a loaf for your special bread. Write a rule to describe your profit as a function of the number n of loaves sold. P(n) = 1.5n - 60

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