Writing a Function Rule ALGEBRA 1 LESSON 5-4 (For help, go to Lesson 5-3.) Model each rule with a table of values. 1. f(x) = 5x – 1 2. y = –3x + 4 3. g(t) = 0.2t – 7 4. y = 4x + 1 5. f(x) = 6 – x 6. c(d) = d + 0.9 Evaluate each function rule for n = 2. 7. A(n) = 2n – 1 8. f(n) = –3 + n – 1 9. g(n) = 6 – n 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 Solutions 1. 2. 3. 4. 5. 6. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 Solutions (continued) 7. A(n) = 2n – 1 for n = 2: A(2) = 2(2) – 1 = 4 – 1 = 3 8. f(n) = –3 + n – 1 for n = 2: f(2) = –3 + 2 – 1 = –1 – 1 = –2 9. g(n) = 6 – n for n = 2: g(2) = 6 – 2 = 4 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 Write a function rule for each table. x ƒ(x) 2 8 4 10 6 12 8 14 a. Ask yourself, “What can I do to 2 to get 8, 4 to get 10, ...?” You add 6 to each x-value to get the ƒ(x) value. Relate:    equals plus 6 Write: = + 6 ƒ(x) x A rule for the function is ƒ(x) = x + 6. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 (continued) b. x y 1 2 2 5 3 10 4 17 Ask yourself, “What can I do to 1 to get 2, 2 to get 5, . . . ?” You multiply each x-value times itself and add 1 to get the y value. Relate:    equals plus 1 Write: = + 1 x2 y x times itself A rule for the function is y = x2 + 1. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 The journalism class makes $25 per page of advertising in the yearbook. If the class sells n pages, how much money will it earn? a. Write a function rule to describe this relationship. Relate:    is  25  times   money earned number of pages sold Define: Let = number of pages sold. n Let = money earned. P(n) Write: = 25 • The function rule P(n) = 25n describes the relationship between the number of pages sold and the money earned. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 (continued) b. The class sold 6 pages of advertising. How much money did the class make? P(6) = 25 • 6 Substitute 6 for n. P(6) = 150 Simplify. P(n) = 25 • n The class made $150. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 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. Relate: is $5.50 times minus cost of tape production total profit tapes sold Define: Let = number of tapes sold. t Let = total profit. P(t) Write: = 5.5 • – 100 The function rule P(t) = 5.5t – 100 describes the profit as a function of the number of tapes sold. 5-4

Writing a Function Rule ALGEBRA 1 LESSON 5-4 1. Write a function rule for each table. x y –1 –5 0 0 1 5 2 10 a. x ƒ(x) –1 –4 0 –3 1 –2 2 –1 b. 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 5-4