PreCalc Function Characteristics part 1

If you've been following my PreCalculus posts you saw that my students started the year by reviewing some function characteristics that they learned in Algebra 2. Now we get into all the other characteristics we use to analyze functions. Basically most of this course is functional analysis.

I have students create notebook pages about the characteristics with foldables and examples they work out.

We started by looking at all the function characteristics they would be learning using this checklist:

We've already done #s 1 - 7. So we move on to Boundedness. We used this foldable to define & explore

 Then asymptotes. Asymptotes can be so interesting. We dabble in them a bit but I'm sure weeks can be spent on this. First we used this foldable to summarize the two main types with a little summary bit on rational functions:

inside:

We did a little pause here and went back to our parent function pages (see this blog post) and filled in who was bounded and what type and who had asymptotes and what type.

 Then we did some examples on the page opposite. The first two examples gave me an opportunity to review transformations a bit when figuring out where those asymptotes were.

Together with the foldable the two-page spread looks like this:

 Then because rational functions are so interesting I decided to do a two-page spread called "crazy rational functions" just so we could see the asymptote options. (unit 2 we do even more with rational functions but I felt like we had to address them a little bit more here).

I used this foldable

We didn't get to finish filling in the whole insde but this is what we did so far (and the examples we'll continue with in our next class):

 I'll then have students do three examples themselves (conferring in their small groups) after we complete the above foldable. The two page spread looks like this:

And a final side note - I really like the information on the coolmath.com site. She handles rational functions in a "fun" way. I get my students using the "king of the top divided by the king of the bottom" to help them figure out the type of asymptotes they should get. See her pages on rational functions here. 

All my function characteristics foldables can be found in this file here.