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Holt Algebra Writing Functions Warm Up Evaluate each expression for a = 2, b = –3, and c = a + 3c 2. ab – c c + b 4. 4c – b 5. b a + c 26 –

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Holt Algebra Writing Functions Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values. Objectives

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Holt Algebra Writing Functions independent variable dependent variable function rule function notation Vocabulary

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Holt Algebra Writing Functions 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.

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Holt Algebra Writing Functions Directions: Identify the independent and dependent variables in the situation.

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Holt Algebra Writing Functions Example 1 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

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Holt Algebra Writing Functions The height of a candle decrease d centimeters for every hour it burns. Dependent: height of candle Independent: time The height of a candle depends on the number of hours it burns. Example 2

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Holt Algebra Writing Functions A veterinarian must weight an animal before determining the amount of medication. The amount of medication depends on the weight of an animal. Dependent: amount of medication Independent: weight of animal Example 3

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Holt Algebra Writing Functions Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable x-values y-values DomainRange InputOutput xf(x)f(x)

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Holt Algebra Writing Functions Example 4 A company charges $10 per hour to rent a jackhammer. The cost to rent a jackhammer depends on the length of time it is rented. Dependent variable: cost Independent variable: time

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Holt Algebra Writing Functions Example 5 Camryn buys p pounds of apples at $0.99 per pound. The cost of apples depends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

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Holt Algebra Writing Functions You can think of a function as an input-output machine. input 10 x function f(x)=5x output 5x5x

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Holt Algebra Writing Functions Directions: Evaluate the function for the given input values.

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Holt Algebra Writing Functions Example 6 For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. = f(7) = 3(7) + 2 Substitute 7 for x. f(x) = 3(x) + 2 = 23 Simplify. f(x) = 3(x) + 2 f(–4) = 3(–4) + 2 Substitute –4 for x. Simplify. = – = –10

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Holt Algebra Writing Functions Example 7 For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2. g(t) = 1.5t – 5 g(6) = 1.5(6) – 5 = 9 – 5 = 4 g(–2) = 1.5(–2) – 5 = –3 – 5 = –8

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Holt Algebra Writing Functions Example 8 For, find h(r) when r = 600 and when r = –12. = 202= – 2

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Holt Algebra Writing Functions Example 9 For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. h(c) = 2c – 1 h(1) = 2(1) – 1 = 2 – 1 = 1 h(c) = 2c – 1 h(–3) = 2( – 3) – 1 = –6 – 1 = – 7

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Holt Algebra Writing Functions Example 10 For g(t) =, find g(t) when t = –24 and when t = 400. = – 5 = 101

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Holt Algebra Writing Functions Lesson Summary: Part I Identify the independent and dependent variables. 1. A buffet charges $8.95 per person. independent: number of people dependent: cost 2. A moving company charges $130 for weekly truck rental plus $1.50 per mile. independent: miles dependent: cost

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Holt Algebra Writing Functions Lesson Summary: Part II Evaluate each function for the given input values. 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31 3. For g(t) =, find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6

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