Functions

 Function has an important impact on algebra. It can be defined as a relation between as set of inputs of permissible output with a property that each input is related to exactly one output. 

There are 3 videos about GeoGebra activity about functions and ideas of students about this activity. In this activity there are 2 shapes. One of them has point a and q maps with 3 points a’ that they can be moved and other one is there is a fixed b which is mapped with b. Therefore, activity is related to which one is function and why, which one is not a function and why by dragging them.

In video 1 there is a student who thinks that I can decide the map between the point a and the points a’ and the map between the fixed-point b and the point b’ according to choosing axis. If we choose x axis with point a and y axis with points a’ the map between the point a and the points a’ is not a function.  So, this student struggles with that issue. 

In video 2 there are two students who think the map between the point a and the points a’ is not a function because point a maps to several different points. On the other hand, according to these students think that the map between the fixed-point b and the point b’ is a function whatever b is b’ still stays whole the time for all values of b. These students do not consider what is the direction of that map. 

In video 3 there is a student who have a question “Is b function even if b’ does not move”. This student struggle about there can be constant function or not.

For machine A is a function because every button gives exactly one and different colors of cokes. 

For machine B is a function because button match with exactly one type coke.  

For machine C is a constant function because all buttons give green cokes. 

For machine D is a function because every button gives exactly one and different colors of cokes. 

For machine E is not function because silver button gives different colors of cokes in two conditions 

- if silver button gives silver cokes

- if silver button gives other colors depending on button which is pressed before silver button.