creat a function machine for a real-word example of a function
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Answer:
Functions in The Real World
When we introduce students to functions, we typically bring the concept to life through the idea of function machines. But functions will really begin to come to life as our students find uses for functions in the real world.
FUNCTION MACHINES
Students easily grasp the idea of a function machine: an input goes in; something happens to it inside the machine; an output comes out. Another input goes in; another output comes out. What's going on inside the machine? If we know the machine's function rule (or rules) and the input, we can predict the output. If we know the rule(s) and an output, we can determine the input. We also can imagine the machine asking, "What's my rule?" If we examine the inputs and outputs, we should be able to figure out the mystery function rule or rules.
We can make that metaphor even more concrete by setting up a large cardboard box with input and output slots. One student sits inside the function machine with a mystery function rule. As other students take turns putting numbers into the machine, the student inside the box sends output numbers through the output slot. After two or more inputs and outputs, the class usually can understand the mystery function rule.
input
output
4
12
5
15
"The function rule: Multiply by 3!"
Options for extending the activity include:
Find the composite function (involving 2 or more function rules).
Include fractions, decimals, and/or negative numbers.
The teacher or the students can create spreadsheet function machines using the formula function.
Students can create function tables for their classmates to solve, with one or two mystery function rules.