Piecewise Functions

We saw piecewise functions earlier in unit 3. We worked with them quite informally as descriptive functions. Then we saw them as a separate function type in the "non-linear" category. Even though the pieces are often linear since there is not a constant rate of change throughout the whole function we're going to classify them as non-linear.

This is a nice introduction worksheet to use when getting students to remember what we did before and what we can do with it now that we've covered linear functions.

Now we look more closely at piecewise functions. Students should be able to graph a piecewise function given the function equations and also to be able to write the function equations for a piecewise graph and finally to evaluate a piecewise function.

We do this two-page spread. I give them the large graph and the function equation slip. We examine the function equation (seeing how each part is defined for a certain domain) and I ask them what those little inequalities might be telling us. Then we use colored pencil or crayon to give each piece a color (highlighting the equation for that piece). And we lightly make vertical lines separating the various parts of the domain. Finally we graph the pieces lightly with pencil (we may need to work "outside of the domain" but then once we get the line we only use the part within the appropriate domain).

ISN large coordinate plane and function equation

Then we make some summary statements about the domain & range. And we go over how to evaluate a piecewise function for given values (notice the color coding). 

This was my first year doing this with students. I gathered a bunch of practice worksheets from on the internet but want to go through those more carefully and create a good packet that students can work on. But here are the sheets I found and mostly used. WS1    WS2    WS3    WS4    exit slip