Function Machine Worksheet Name: ________________________ Period: _______ Part I. Function Machine Model & Guided Instruction. How to find the output, when you know the input and function of the machine. A. The rule for the input-output machine is: Output = 2·input – 3. I. If you input 3 into the function machine, then what is the output? ____ II. If you input –5 into the function machine, then what is the output? ____ How to find the function when you know the inputs and outputs. If the input is –2, the output is 7. If the input is 1, the output is –2. If the input is 3, the output is –8. B. What is the input-output rule for the function machine? _____________ Real life application. C. Can you make a machine that applies to your life? Example: Perhaps the price of all the items in your favorite store has increased by 10%. What would be the input-output rule for a 10% increase? Part II. Determine the function. A. We will be using the following website to complete the following tables. If you need additional practice with writing functions please use this website from home. http://www.mathplayground.com/functionmachine.html X Y X Y X Y X Y Y = __________ Y = __________ Y = __________ Y = __________ Part III. Tables. A. What kind of numbers can be inputs? Are there any situations where the numbers for the inputs are limited? B. What kind of numbers can be outputs? Are there any situations where the numbers for the outputs are limited? C. How does the output depend on the rule? D. If you restrict the inputs to only even numbers, then how would it change the outputs? Why? Part IV: Comparing Rules For each sequence below write the NOW-NEXT and INPUT-OUTPUT equation. Sequence NOW-NEXT Rule INPUT-OUPUT Rule Example 1 Term Value 1 5 2 8 3 11 4 14 5 17 Example 2 Term Value 1 52 2 46 3 40 4 34 5 28 Compare and Contrast Recursive (NOW-NEXT) and Explicit (INPUT-OUTPUT or Y = ) rules with your group. Focus on discussing the following questions 1) What information can you get from each form? 2) When is it more advantageous to use one form vs. the other?