Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 3 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 3 — Use function notation to evaluate functions and describe domain and range; perform operations on functions and composition.

This file holds two pieces: (A) the Module 3 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 3 meeting Tue Sep 15 and Thu Sep 17, and end-of-week work due Sunday Sep 20, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 3 Overview — Start Here

Welcome to Week 3: Functions — Notation, Domain & Range

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Two weeks in, you can simplify expressions and solve equations. Now we ask: what does algebra do? The answer is a function — a rule that takes an input and produces exactly one output. Functions are the central object of every remaining week in this course, so the ideas you build here will pay dividends all term.

The week's big question

"Given a rule, what can I plug in, what can I get out, and how do I combine two rules into one?"

By Sunday you'll read f(x) as a rule (not a product), find f(a + 2) without hesitation, state the domain of any polynomial, rational, or radical function, perform all four arithmetic operations on functions, and compose two functions — feeding one's output into the other as input.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Identify a function using the definition (each input → exactly one output) and the vertical line test, and evaluate f(x), f(−2), and f(a + 2) using the correct substitution.
• [ ] State the domain of any polynomial (all reals), rational function (exclude denominator zeros), or radical function with an even root (radicand ≥ 0); state the restricted domain of a quotient f/g.
• [ ] Perform the four operations on functions — (f + g)(x), (f − g)(x), (fg)(x), (f/g)(x) — and identify any new domain restrictions.
• [ ] Compose two functions — (f ∘ g)(x) = f(g(x)) — and evaluate at a specific input; explain why order matters (f ∘ g ≠ g ∘ f in general).

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: the classic trap here is reading f(x) as f times x. The chatbot sometimes makes this exact mistake — part of the tutorial is catching it.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Read f(x) as "f of x," never "f times x." The parentheses denote substitution, not multiplication. This misreading causes more Week-3 errors than any algebra slip.
• Substitute carefully, especially with f(a + 2). Write the entire input inside parentheses everywhere x appears before simplifying: f(a + 2) = 3(a + 2) − 1, then expand. One step at a time.
• Domain is about what's forbidden, not what's allowed. For rationals, set the denominator equal to zero and exclude those values. For even roots, set the radicand ≥ 0. Polynomials have no restrictions.
• Composition: work from the inside out. (f ∘ g)(x) means do g first, then feed the result into f. Right-to-left, inside-to-outside — not the other way.
• Use Desmos to visualize. Graph f(x) and g(x) separately; then graph (f ∘ g)(x) and compare. Seeing functions as curves reinforces everything you're computing this week.

You've already done the heavy lifting on algebra — this week is about giving it shape and direction. See you Tuesday.

(B) Welcome Announcement — Module 3

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Sep 14, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Sep 14."

Subject: Week 3 — The rule that makes algebra into a machine 🔧

Hi everyone,

Quick question: when you enter a price into a tax calculator and the total pops out, what just happened? You gave the calculator an input and it handed you exactly one output — a function. That's exactly what we're studying this week: how to read, evaluate, and combine those rules.

This week — Functions: Notation, Domain & Range — we tackle the big question: Given a rule, what can I plug in, what can I get out, and how do I combine two rules into one? By Sunday you'll evaluate f(a + 2) without blinking, know instantly whether a function is defined at a given input (domain), and compose two functions like chaining two machines together.

Three things not to miss:
1. Lecture Tutorial 3 — work through the week's ideas with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. You'll catch the classic chatbot error: it sometimes reads f(x) as multiplication. Due Sun Sep 20.
2. Quiz 3 (no AI on quizzes) and Discussion 3 — "Is It a Function? What Goes In?" also close Sun Sep 20 — the discussion is a quick AI dialogue about a real-world input→output relationship, so start early and leave time to reply to classmates.
3. Assignment 3 — four AI-coached problems with a self-scored report; due Sun Sep 20.

One promise for this week: every idea is a plain-language idea first. "Domain" just means "what you're allowed to plug in." "Composition" just means "chain two rules together." The notation follows the idea — never the other way around.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. See you Tuesday.

Prof. Calloway