PreCalculus 1st six weeks Project

Pre-Calculus                 1st Six Weeks Project  


A Library of Parent Functions           Due Thursday, September 30

Part 1

1.      You will create a library of functions to use as a reference tool.  The library must include linear, quadratic, cubic, square root, exponential, and logarithmic functions.  Please show exponential functions with base 2 and base ½.  You should show logarithmic functions with base 10 and with base e.

2.      For each function:

a.       Write the equation of the parent function.

b.      Write the different forms of the equation of the function. 

                                                                           i.      Ex:  For quadratics you should write the forms:

1.      y = a(x-h)2+k


2.      y = ax2+bx+c


c.       Sketch a graph of the parent function and another function in each family.

Part 2

1.  For linear and quadratic functions, you will write an explanation of how to determine transformations.  You must discuss:  vertical and horizontal translations, vertical and horizontal stretches and compressions, and reflections across both the x-axis and y-axis.


2.  Discuss how the transformations of linear and quadratic functions relate to other functions.  For any given function, how do you determine the type of transformation taking place?



Task                                                    Points Possible           Points Earned

Part 1  

            Write equation of parent function

 and different forms of function                          20                    _________


            Sketch graphs of parent function                       15                    _________


            Sketch graph of another member

            of each family                                                   15                    _________


Part 2

            Discussion of linear transformations                   10                    _________


            Discussion of quadratic transformations             10                    _________


            Discussion of relationship between

            linear and quadratic transformations and

            other transformations                                        15                    _________

            Answer to the question of how to determine

            transformations for any given function                15                    _________


                                                Total                           100                  _________


*10 points will be taken off for each day the project is late.  No projects will be accepted after Friday, October 1st.