Transformations of Functions

Students were put in visible random groups of three alphabetically by first name. They brainstormed all the transformations they could remember and filled in a chart with three columns.
1) a description of the transformation
2) the function mapping f(x) --->
3) the ordered pair mapping (x,y) --->

We consolidated this as a class.

We talked about all the different types of functions we have been introduced to.

At this point each group was given a base function and were asked to do this.

 

So basically for their base function they would perform 5 transformations as listed above and create 6 graphs on the same grid. first one would be the base function, then the second one would have one transformation applied to it, then the third one would have two transformations applied to it, and so on until the sixth graph which would have 5 transformations applied to it.

 

Some student work for polynomials (y=x^3): 



 



 

 

 

 

Student work for y=absolute value of x







 



Some student work for y=1/x.

 

 

 

Some student work for the square root function.

 

 

 

 

Some student work for exponential functions.

 

 



 

 

Some student work for Trigonometric functions sine and cosine.

 



 

 

 

 

 

 

 

 

Eventually all groups final equations were written on the whiteboards and groups had to graph the other four curves - excluding their own. Here are the four samples of 5 equations.





 

 

A little demonstration on how to get the final table of values.

 Student's work on the four graphs.

My work for a set of 5 graphs - in 40 minutes for those of you who thought it was too much work!

Review work for the upcoming test.