Using lab explorations to introduce functions in Algebra provides engagement as well as data collection analysis activities. Students use everyday materials to collect data. The data describes specific functions. Here are a collection of "lab" activities I've tried in the past few years:
Linear (and Quadratic) Function: Pass the Ball
All the information needed for this activity is in this blog post. Students pass a ball to one person, timing the event. Then to two people, three people, etc. This is a very easy lab to set up.
Both of these activities are simple, table top activities that result in quadratic patterns. I provide instructions in this blog post.
Exponential Functions: M 'n M Data Collection
This is popular for obvious reasons - students love to eat the m 'n ms after the experiment is complete. We do both parts ... exponential growth and decay. I wrote a short blog post - without any real helpful information here and also here. The handouts with instructions can be found here and here.
Rational Functions: Spaghetti Cantilevers
Instructions are online. Students bundle 2, 3, 4, 5, 6 pieces of spaghetti and hang a weight from the end without breaking the spaghetti. They collect the data and analyze it. The rational function is the model for the cantilever. I write a blog post about this lab here. And took a few pictures: