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**Warm Up Evaluate each expression for a = 2, b = –3, and c = 8.**

2. ab – c 3. 26 –14 1 2 c + b 1 4. 4c – b 35 5. ba + c 17

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**Objectives Identify independent and dependent variables.**

Write an equation in function notation and evaluate a function for given input values.

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**Vocabulary independent variable dependent variable function rule**

function notation

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**The input of a function is the independent variable**

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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**Directions: Identify the independent and dependent variables**

in the situation.

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

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Example 3 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

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

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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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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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**You can think of a function as an input-output machine.**

x 2 You can think of a function as an input-output machine. 6 function f(x)=5x 5x 10 30 output

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Directions: Evaluate the function for the given input values.

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Example 6 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(7) = 3(7) + 2 f(–4) = 3(–4) + 2 = Simplify. Simplify. = –12 + 2 = 23 = –10

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

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

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

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

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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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**Lesson Summary: Part II**

Evaluate each function for the given input values. 3. For g(t) = , find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31

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