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5-4: Writing a Function Rule Objectives: You will write function rules to describe given situations. Given a table and/or graph of a function, you w ill write a function rule that describes that function. What’s my rule? Ask different students to give you numbers between 1 & 50, and tell them the output. Then they must guess the rule. 1. f(x) = x + 2 2. f(x) = 2x 3. f(x) = 2x – 10 Writing a function rule from a situation EX 1: Suppose you borrow money from a relative to buy a lawn mower that costs $245.You charge $18 to mow a lawn. Write a rule to describe your profit as a function of the number of lawns mowed. EX 2: Suppose you buy a word-processing software package for $199. You charge $15 per hour for word processing. Write a rule to describe your profit as a function of the number of hours you work. EX 3: A zucchini plant in Keith’s garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 cm per day. a. Write a rule to describe the function. H(d) = 0.5d + 10 b. When will the plant be 0.185 meters tall? After 17 days. Writing a function rule from a table Ask yourself – “What can I do to x to make it equal f(x)?” Hint—Look at when x = 0, and at the change between x and y values. Write a function for each table EX 1: f(x) = x + 4 x f(x) 0 4 1 5 2 6 3 7 4 8 EX 2: f(x) = -2x x f(x) -2 4 -1 2 0 0 1 -2 2 -4 EX 3: f(x) = 0.5x x f(x) 0 0 1 0.5 2 1 3 1.5 4 2 EX 4: f(x) = -3x + 10 x f(x) -4 22 -3 19 -2 16 -1 13 0 10 EX 5: f(x) = 3x+1 x f(x) 0 0 1 0.5 2 1 3 1.5 4 2 EX 5: f(x) = x2 x f(x) -4 16 -1 1 0 0 1 1 3 9 Writing a function rule from a graph EX 1: f(x) = 3x EX 2: f(x) = ½ x – 1