Transformation of Functions

This interactive excel program allows students to explore the relationship between the transformation of functions and the associated graphs. Functions explored are straight lines, quadratic and cubic functions as well as sine and cosine curves. Each type of function can be fully transformed in stages. The algebraic expression for each function can be hidden or revealed. By selecting "new" the interactive sheets present the student with the graph of a new function so understanding can be tested.

The form of the quadratic function is a(x+b)²+c. The parameters can be increased or decreased to transformed from f(x)=x². After each transformation the intermediate graph remains visible. Hence the full picture of the steps towards each composite transformation is revealed.

The interactive sheets for the sine and cosine functions deal with the forms asin(x+b)+c and acos(x+b)+c. The parameters can be changed and the graphs of intermediate functions revealed. New functions can be generated and the algebraic expression revealed.

The resource also has 12 sheets of printable sets of questions which may be suitable for use within the classroom.

Note:

This program was designed to be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on a machine.