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.