5-4: Writing a Function Rule

1. Saint Agnes Academy Text Resource: Prentice Hall 5-4: Writing a Function Rule This lesson has two parts: Look at a table of values, find a pattern, and write the function rule (equation) that describes the pattern. Translate a real world problem into a function rule (equation).

2. Saint Agnes Academy Text Resource: Prentice Hall Look for the pattern and write the function rule. y = something done to the x. 5 = Something done to 1. 1 + 4…does this work for the other x’s? y = x + 4 6 = 2 + 4 7 = 3+ 4 8 = 4 + 4 YES! y = x + 4 is the function rule!

3. Saint Agnes Academy Text Resource: Prentice Hall Look for the pattern and write the function rule. y = something done to the x. 1 = Something done to 1. 12…does this work for the other x’s? y = x2 9 = 32 36 = 62 81 = 92 YES! y = x2 is the function rule!

4. Saint Agnes Academy Text Resource: Prentice Hall ALGEBRA 1 LESSON 5-4 Writing a Function Rule Write a function rule for each table. ƒ(x) = something done to the x. 8 = Something done to 2. 2 +6…does this work for the other x’s? y = x+ 6 10 = 4+ 6 12 = 6+ 6 14 = 8+ 6 YES! y = x+ 6 is the function rule! 5-4

5. xy 1 2 2 5 3 10 4 17 Relate:    equals plus 1 Write: = + 1 y x times itself y x2 Saint Agnes Academy Text Resource: Prentice Hall ALGEBRA 1 LESSON 5-4 Writing a Function Rule (continued) You try one! b. 2 = something done to 1 5 = something done to 2 10 = something done to 3 A rule for the function is y = x2 + 1. 5-4

6. money earned number of pages sold Relate:    is  25  times   n Define: Let = number of pages sold. P(n) Let = money earned. P(n) n Write: = 25 • Saint Agnes Academy Text Resource: Prentice Hall ALGEBRA 1 LESSON 5-4 Writing a Function Rule 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. The function rule P(n) = 25n describes the relationship between the number of pages sold and the money earned. 5-4

7. Saint Agnes Academy Text Resource: Prentice Hall ALGEBRA 1 LESSON 5-4 Writing a Function Rule (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

8. total profit tapes sold Relate: is $5.50 times minus cost of tape production t Define: Let = number of tapes sold. P(t) Let = total profit. P(t) t Write: = 5.5 • – 100 Saint Agnes Academy Text Resource: Prentice Hall 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. Profit = selling price - cost The function rule P(t) = 5.5t – 100 describes the profit as a function of the number of tapes sold. 5-4

9. xy –1 –5 0 0 1 5 2 10 x ƒ(x) –1 –4 0 –3 1 –2 2 –1 a. b. Saint Agnes Academy Text Resource: Prentice Hall ALGEBRA 1 LESSON 5-4 Extra Practice 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 5-4