In mathematics, a function is derived as one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function machine is a way of visualizing functions and their inputs and outputs.
Students should know how to recognize how things change in relation to each other. Teacher should also concentrate on the difference between qualitative and quantitative change. One is involved with quantity change while the other one is the attribute change.
As the student moves through the years, functions will begin to move from the concrete to the abstract, and finally, standard representation Willoughby (1997). The example below shows the standard representation used in function.
Starting off with number 2 moves through the function machine and comes out number 6. Next number 9 goes through the function machine and number 20 come out. The unidentified number goes through the function machine and comes out number 16. Lastly, number 6 goes in through the function machine and number 14 comes out. Students will found out that the function doubles the number that goes in which is the input, and adds 2 to give the end product of the machine which is the output. Thus, the answer to the number 4th machine is 7 because as it doubles up and adds 2, the output is 16.
Qualitative Change
Q: What shape will comes out next on the blue row ?
A: A blue circle.
The picture below shows the function machine with the input of circle and the output of a big triangle with different colour. When the yellow circle goes into the machine, a big yellow triangle come out as the output of the machine. Similar steps goes for the second one but with different colour instead, now it is green.
Q: What is the output of the blue circle as it goes into the function machine?
A: A big blue triangle.
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