Composite Functions

Whether you introduce composite functions in Math 3 or Precalculus, here are a couple of options to spice up your lesson!

Option 1

I like using this activity in my Precalculus class as an introduction to composite functions. This could be used as an exit slip on day 1 of teaching this topic or a stand alone activity on day 2.

Part A (Number Line) has students evaluating composite functions with specific values then arranging the slides in numerical order.

Part B (Cut and Paste) uses two functions: f(x) and g(x). Students are to evaluate both f(g(x)) and g(f(x)); if they are correct, they will find their answer on the final slide of the presentation. Students will cut the answers and place it in the appropriate location for that problem. If the learners are incorrect, their answers will (probably) not be found and they will need to redo the problem to find their mistake.

Here is the key for this activity.

Option 2

I used this activity as a project and allowed students to work with a partner.

Part 1 has students creating their own functions (3 of them) with at least two operations each; you can modify the specifications to fit your learners. Once functions are created, students must go through a series of composites to evaluate.

Part 2 is decomposition. Again, students are asked to create their own functions, 5 this time, each with only one operation. They are then asked to compose a function and then write it in decomposed form.

Part 3 is completely stolen from Google and has been sitting in my Drive for years- I have no idea who created it. Students are given pairs of names and asked to compose different variations. I did modify the original to fit my students' learning targets.

Composite away!

~ssb

Comments

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