Assisting Teacher Handoff Sheet

Session 2.1 - Domain of Functions | Week 2, Tuesday

FOR THE ASSISTING TEACHER: Read the information below before Kaa Shaayi leaves at 2:00. You are supervising worksheet time from 2:00-3:00. Students work independently from 3:00-3:30.

What Students Just Learned (30-second summary)

The domain is the set of all valid inputs for a function. Two things break functions: dividing by zero (denominator can't be 0) and square root of a negative (expression under √ must be ≥ 0). Linear and quadratic functions never break; their domain is all real numbers.

The Worksheet

Worksheet 2.1 (35 points, 8 problems across 4 parts). The Quick Reference box at the top includes an interval notation cheat sheet. Students do NOT need to have this memorized; they can look at the table while they work.

Part A (Story): Real-world domains - area of a square, temperature conversion, book pages. Students give both mathematical and contextual domains.

Part B (Visual): Graphing functions in Desmos and observing where graphs exist or disappear. Students need access to desmos.com/calculator.

Part C (Traditional): Finding domain algebraically - setting denominators ≠ 0 and radicands ≥ 0. Plus interval notation practice.

Part D (Synthesis): Summary table of domain rules by function type, and a written explanation.

Top 3 Mistakes to Watch For

1. Mixing up mathematical vs. contextual domain.
For A(s) = s² (area of a square), math says any number works, but side length can't be negative. Students sometimes give only one domain. Push them: "What does the algebra allow? Now what makes real-world sense?"
2. Forgetting to factor in Problem 5d.
f(x) = 3/(x² - 16). Students need to factor: x² - 16 = (x-4)(x+4), so x ≠ 4 and x ≠ -4. Many only find one value.
3. Interval notation brackets.
Students confuse [ ] (includes endpoint) with ( ) (excludes endpoint). Infinity ALWAYS gets parentheses. The Quick Reference table at the top of the worksheet has examples you can point them to.

If a Student Is Stuck

First: Point them to the Quick Reference box, which has the two domain rules and the interval notation table.

Second: Ask: "Does this function have a fraction or a square root? If yes, that's where the restriction comes from. If no, the domain is all real numbers."

Third: For Desmos problems, have them type the function in and look at where the graph appears. The visual makes the algebra click.

Video: Organic Chemistry Tutor "How To Find The Domain" on YouTube (18-minute walkthrough linked in the Reading).

Priority Problems

If students are running low on time: Problems 1, 3, 5, 7 (one from each part). The summary table (Problem 7) is especially useful as a study reference; encourage them to complete it even if they skip other problems.