holt algebra 1 4-3 writing functions warm up evaluate each expression for a = 2, b = –3, and c =...

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Holt Algebra 1 4-3 Writing Functions Warm Up Evaluate each expression for a = 2, b = – 3, and c = 8. 1. a + 3c 2. ab c 3. 1 2 c + b 4. 4c b 5. b a + c 26 –14 1 35 17

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Holt Algebra 1 4-3 Writing Functions Warm Up Evaluate each expression for a = 2, b = 3, and c = 8. 1. a + 3c 2. ab c 3. 1212 c + b 4. 4c b 5. b a + c 26 14 1 35 17 Slide 2 Holt Algebra 1 4-3 Writing Functions Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values. Objectives Slide 3 Holt Algebra 1 4-3 Writing Functions independent variable dependent variable function rule function notation Vocabulary Slide 4 Holt Algebra 1 4-3 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. Slide 5 Holt Algebra 1 4-3 Writing Functions Directions: Identify the independent and dependent variables in the situation. Slide 6 Holt Algebra 1 4-3 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 Slide 7 Holt Algebra 1 4-3 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 Slide 8 Holt Algebra 1 4-3 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 Slide 9 Holt Algebra 1 4-3 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) Slide 10 Holt Algebra 1 4-3 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 Slide 11 Holt Algebra 1 4-3 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 Slide 12 Holt Algebra 1 4-3 Writing Functions You can think of a function as an input-output machine. input 10 x function f(x)=5x output 5x5x 6 30 2 Slide 13 Holt Algebra 1 4-3 Writing Functions Directions: Evaluate the function for the given input values. Slide 14 Holt Algebra 1 4-3 Writing Functions Example 6 For f(x) = 3x + 2, find f(x) when x = 7 and when x = 4. = 21 + 2 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. = 12 + 2 = 10 Slide 15 Holt Algebra 1 4-3 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 Slide 16 Holt Algebra 1 4-3 Writing Functions Example 8 For, find h(r) when r = 600 and when r = 12. = 202= 2 Slide 17 Holt Algebra 1 4-3 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 Slide 18 Holt Algebra 1 4-3 Writing Functions Example 10 For g(t) =, find g(t) when t = 24 and when t = 400. = 5 = 101 Slide 19 Holt Algebra 1 4-3 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 Slide 20 Holt Algebra 1 4-3 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