Piecewise functions
Students have already explored these in Algebra 1 & 2. They should remember what they are, how to graph them and how to evaluate values in a piecewise function. I know in my Algebra 1 class we do some real life examples too so students see where piecewise might make sense.
Here we do a tiny little review but then really look at piecewise in the context of continuity (and determining the domain & range).
We do a notes page in our interactive student notebooks (ISNs). Then students try to create a piecewise picture on their graphing calculator given instructions.
After that we create an ISN page showing our results.
Students were pretty excited about this.
And I use this opportunity to plug my "graphing calculator project" that they get in December. In this project they draw a picture on their calculator with pieces of functions. At least 30 pieces, usually more like 50 or so. It's a great project. Will blog about it later. Students love it. And it's really time consuming. But great.
Okay, now we've reviewed piecewise functions and have covered rational functions. We can now ease into what "continuity" means. We really do this more visually than anything else. But we do categorize the types of discontinuity.
We start with a foldable of course, in our ISN.
We fill the inside in. I use my document camera to project and fill things in with the students.
Behind the left two doors:
and the right two doors:
And then on their "right side reflect" page opposite this foldable students work through 4 examples. Here is the work for those examples:
From here they have some homework and two classes from now I'll be giving an assessment to see how they are at analyzing functions with the tools we have so far (domain, range, boundedness, asymptotes, continuity).
And part 3 will be looking at the basics of limits & describing end behavior with limit notation. After that part 4 is symmetry in functions (even vs odd).
Foldable documents can be found here.
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