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3.3 Notes Alg1.notebook October 25, 2012 33 Writing Functions Skills we've learned 1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram. 2. Give the domain and range of the graph: Skills we need 3. Write an equation: "Cost of a book is $8 per book." 4. If f(x) = x + 2, what is f(3)? Warmup Answers 3. Write an equation: "Cost of a book is $8 per book." 4. If f(x) = x + 2, what is f(3)? c = 8b 5 3.3 Notes Alg1.notebook October 25, 2012 33 Writing Functions 1. Identify independent and dependent variables 2. Write an equation in function notation. 3. Evaluate using function notation. Calculating how much money you will earn for working specific amounts of time. I. Using a Table to Write an Equation 1. Determine a relationship between the x and yvalues. Write an equation. Step One Possibilities: Step Two check for consistency: Answer: 3.3 Notes Alg1.notebook October 25, 2012 2. Determine a relationship between the x and yvalues. Write an equation. {(1, 3), (2, 6), (3, 9), (4, 12)} Step One 1 • 3 = 3 or 1 + 2 = 3 Step Two Answer y = 3x The value of y is 3 times x. II. Identifying Independent & Dependent The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable. Identify the independent and dependent variables in the situation. 3. A painter must measure a room before deciding how much paint to buy. The amount of paint depends on the measurement of a room. Dependent: amount of paint Independent: measurement of the room 3.3 Notes Alg1.notebook October 25, 2012 4. The height of a candle decreases d centimeters for every hour it burns. Dependent: ___________ Independent: __________ 5. A veterinarian must weigh an animal before determining the amount of medication. Dependent: ___________ Independent: __________ 6. A company charges $10 per hour to rent a jackhammer. Dependent: ___________ Independent: __________ 7. Apples cost $0.99 per pound. Dependent: ___________ Independent: __________ III. Writing Functions When an equation in two variables describes a function, you can use function notation to write it. The dependent variable is a function of the independent variable. y is a function of x. y = f (x) y = f(x) 8. 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 is f(h) = 35h. 3.3 Notes Alg1.notebook October 25, 2012 9. A fitness center charges a $100 initiation fee plus $40 per month. function:_____________ 10. Steven buys lettuce that costs $1.69/lb. function:_____________ 11. An amusement park charges a $6.00 parking fee plus $29.99 per person. function:_____________ V. Evaluating Functions 12. 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. f(7) = 3(7) + 2 f(7) = 21 + 2 f(7) = 23 Substitute –4 for x. f(–4) = 3(–4) + 2 f(–4) = 12+ 2 f(–4) = 10 3.3 Notes Alg1.notebook October 25, 2012 V. Evaluating Functions 13. Evaluate the function g(t) = 1.5t – 5 when t = 6 and when t = –2. g(t) = 1.5t – 5 g(t) = 1.5t – 5 g(6) = 1.5(6) – 5 = 9 – 5 = 4 g(–2) = 1.5(–2) – 5 = –3 – 5 = –8 VI. Finding the Reasonable Domain and Range When a function describes a realworld situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people. 14. Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each, if he buys any at all. a. Write a function to describe the situation. If Joe buys x DVDs, he will spend f(x) = 15x dollars. b. Find the reasonable domain of the function. Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {0, 1, 2, 3}. c. Find the reasonable range of the function. Substitute the domain values into the function rule to find the range values. A reasonable range for this situation is {$0, $15, $30, $45}. 3.3 Notes Alg1.notebook October 25, 2012 VI. Finding the Reasonable Domain and Range 15. The settings on a space heater are the whole numbers from 0 to 3. The total number of watts used for each setting is 500 times the setting number. a. Write a function to describe the situation. b. Find the reasonable domain of the function. c. Find the reasonable range of the function. 33 p.183 #3 11 all, 12 27 (x3), 28, 30, 33 35 all