Written as a request for a colleague, this circuit contains 20 problems which give students practice in evaluating functions and doing all sorts of operations with functions both symbolically and numerically. Addition, Subtraction, Multiplication, Division, and Composition of functions are all covered. The target audience is algebra two, but I could imagine strong algebra one students working this circuit (with a short lesson on notation first) or college algebra / low level precalculus students working this circuit.
To advance in the circuit, students must search for their answer. This keeps them engaged! Talking! Excited! My students do not get up when the bell rings if they are working on a circuit. This circuit can easily be made into an around the room scavenger hunt.
There is no answer key included because the answers are imbedded in the circuit (it is how students move from one problem to the next -- the problems are progressive in nature). The only prep the teacher needs to do is work the circuit ahead of the students to see what kind of guided notes/examples should be given before setting the students free on the circuit.
My colleagues and I check our circuits very carefully but should you ever find a mistake or get stuck, please do not hesitate to contact me at firstname.lastname@example.org.