Here are some activities that I may or may not have blogged about, but have proven successful in my precalculus classroom.
“Functions ‘Reversed'” Activity – Many activities and problem sets ask students to find the domain and range of a function. This activity asks students to write functions based on certain domain and range criteria. PDF Version Pages Version
“Operations on Functions” Inquiry – It turns out that when you combine functions using different operations you can make predictions on what the functions will looks like based on the “combined functions”. This is especially true when the functions are from different families. This activity asks students to look at the functions as a whole and then in parts and describe how they could predict what the graph would look like based on the partial functions. This takes a topic that can seem dry and pointless and gives it meaning. I heard lots of “Oh that is cool” during this activity. (Made in collaboration with Steve Kelly) PDF Version Pages Version
“Connecting Zeros, Factors, and Polynomial Division” Activity: This is an activity that is designed to help students see the connection between the zeros of a polynomial function, the factors of the function, and how polynomial division fits into everything. This went over well in class and I had almost complete engagement when students were going through it. This activity also encourages students make conjectures about repeated zeros. PDF Version Pages Version