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Activity 3.2 Changes in Input and Output Overview: A table of values of miles driven and the number of gallons of gas used is given and students are asked to explain what different function notation values represents. Estimated Time Required: This activity should take approximately 20 minutes. Technology: None Concepts: Evaluating a function using function notation The effects of addition to input and output Discussion: A major goal of the course is to move students towards a more global view of functions as objects that model particular situations. You may want to discuss the interpretive aspects of function notation and language, as shown in Example 2 and 3 in the text, before given students the activity. Activity 3.2 Changes in Input and Output Problem 1 A car averages 20 miles per gallon of gas. Complete the table below. m = number of miles driven n = number of gallons of gasoline used m n = f(m) f(m+30) f(m) + 30 0 0 1.5 30 Explain what f(m + 30) means. Explain what f(m) + 30 means. 20 1 2.5 31 40 2 3.5 32 60 3 4.5 33 80 4 5.5 34 100 5 6.5 35 Problem 2 Now consider g, as a function of the number of gallons. n m = g(n) g(n+30) g(n) +30 1 20 620 50 Explain what g(n + 30) means. Explain what g(n) + 30 means. 2 40 640 70 3 60 660 90 4 80 680 110 5 100 700 130 6 120 820 150