3-3

1. 3-3 Writing Functions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

2. 1 2 c + b Warm Up Evaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3c 2.ab– c 3. 4. 4c – b 5. ba + c

3. Objectives Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.

4. 5 – 4 = 1 or Example 1: Using a Table to Write an Equation Determine a relationship between the x- and y-values. Write an equation. 5 10 15 20 1 3 2 4 Step 1 List possible relationships between the first x or y-values.

5. 10 – 4 2 and 15 – 4 3 and 20 – 4 4 and The value of y is one-fifth, , of x. or Example 1 Continued Step 2 Determine if one relationship works for the remaining values. Step 3 Write an equation. The value of y is one-fifth of x.

6. Now you try!!! Determine a relationship between the x- and y-values. Write an equation. {(1, 3), (2, 6), (3, 9), (4, 12)} x 4 1 2 3 y 3 6 9 12 The equation in this example describes a function because for each x-value (input), there is only one y-value (output).

7. Pick a number from the following list. Without leaving your seat, find another person around you with another number. Write down at least two different ways to relate those two numbers. Be creative. Figure out which would be x and which would be y. Repeat with another person around you. 48 29 38 42 13 6 72 7 37 18 9 21 52 4 10 31 16 38 15 54 62 11 2 46 3 5 22 70 32 25 102 50 58 80 28 17 8 1 64 92

8. VOCABULARY Independent Variable: The inputof a function. Dependent Variable: The output of a function. * The value of the dependent variable depends on, or is a function of, the value of the independent variable.

9. Example 2A: Identifying Independent and Dependent Variables Identify the independent and dependent variables in the situation. A painter must measure a room before deciding how much paint to buy. The amount of paintdependson the measurement of a room. Dependent: amount of paint Independent: measurement of the room

10. Example 2B: Identifying Independent and Dependent Variables Identify the independent and dependent variables in the situation. The height of a candle decreases d centimeters for every hour it burns. The height of a candledepends on the number of hours it burns. Dependent: height of candle Independent: time

11. Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable y-values x-values Domain Range Input Output x f(x)

12. Try These Two!!! Identify the independent and dependent variable in the situation. A company charges $10 per hour to rent a jackhammer. Apples cost $0.99 per pound.

13. FUNCTION NOTATION The dependent variableisa function ofthe independent variable. yisa function ofx. y=f(x) y = f(x)

14. Example 3A: Writing Functions Identify the independent and dependent variables. Write an equation in function notation for the situation. A math tutor charges $35 per hour. The fee a math tutor charges depends on number of hours. Dependent: fee Independent: hours Let h represent the number of hours of tutoring. The function for the amount a math tutor charges isf(h) = 35h.

15. Example 3B: Writing Functions Identify the independent and dependent variables. Write an equation in function notation for the situation. A fitness center charges a $100 initiation fee plus $40 per month. The total cost depends on the number of months, plus $100. Dependent: total cost Independent: number of months Let mrepresent the number of months The function for the amount the fitness center charges is f(m) = 40m + 100.

16. Give this a Try!! Identify the independent and dependent variables. Write an equation in function notation for the situation. An amusement park charges a $6.00 parking fee plus $29.99 per person.

17. You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x. input x 2 6 function f(x)=5x 5x 10 30 output

18. Example 4A: Evaluating Functions Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. f(x) = 3(x) + 2 f(x) = 3(x) + 2 Substitute 7 for x. Substitute –4 for x. f(–4) = 3(–4) + 2 f(7) = 3(7) + 2 Simplify. = –12 + 2 = 21 + 2 Simplify. = 23 = –10

19. Try this one!! Evaluate the function for the given input values. For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.

20. Money spent is$15.00 for each DVD. Example 5: Finding the Reasonable Domain and Range of a Function Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each, if he buys any at all. Write a function to describe the situation. Find the reasonable domain and range of the function. f(x)=$15.00• x If Joe buys x DVDs, he will spend f(x) = 15x dollars. Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {0, 1, 2, 3}.

21. x 1 2 3 f(x) 15(1) = 15 15(2) = 30 15(3) = 45 Example 5 Continued Substitute the domain values into the function rule to find the range values. 0 15(0) = 0 A reasonable range for this situation is {$0, $15, $30, $45}.

22. HOMEWORK PG.183-185 #13-35 (skip 27,28)