# 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?

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

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.