Week 3 — Readings & Resources · Functions: Notation, Domain & Range

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 3 — Use function notation to evaluate functions and describe domain and range; perform operations on functions and composition.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~3 readings + ~3 videos, grouped by the three main ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–60 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① what is a function + notation + evaluating → ② domain & range → ③ operations on functions + composition.

A habit to start now: the AI tutorial this week ends by having you catch a chatbot reversing the composition order. Keep that posture as you read — the tool drafts, you check.

① Functions, Function Notation & Evaluating

Maps to Lecture Segments 2–3. The definition of a function, the vertical line test, and how to evaluate f(x) at numbers and algebraic expressions like f(a + 2).

Reading — "Functions and Function Notation" (OpenStax, College Algebra 2e, §3.1)
🔗 https://openstax.org/books/college-algebra-2e/pages/3-1-functions-and-function-notation
Why it's assigned: the most thorough free treatment of the function definition, mapping diagrams, the vertical line test, and function notation — with worked examples of evaluating at numbers, expressions, and algebraic inputs. Matches the lecture closely.
⏱ ~12 min

Video — "Introduction to Functions" (Professor Leonard, Precalculus — College Algebra series)
🔗 https://www.youtube.com/watch?v=FkUEsP9efFg
Why it earns the click: an unhurried, board-worked introduction to what a function is, how to read function notation, and how to evaluate — ideal if you want to see every step at a teacher's pace.
⏱ longer lecture (skim to the parts you need)

② Domain & Range

Maps to Lecture Segment 4. The three domain rules: polynomial = all reals; rational = exclude denominator zeros; even root = radicand ≥ 0.

Reading — "Domain and Range" (OpenStax, College Algebra 2e, §3.2)
🔗 https://openstax.org/books/college-algebra-2e/pages/3-2-domain-and-range
Why it's assigned: walks through how to find the domain of polynomials, rational functions, and radical functions — with the same three-case approach used in class, plus worked examples and interval notation.
⏱ ~10 min

Video — "Finding the Domain of Functions" (Professor Leonard, Precalculus — College Algebra series)
🔗 https://www.youtube.com/watch?v=LvUCDcp6Z3k
Why it earns the click: a full-length walkthrough of domain-finding for all the function types you'll encounter this week and all term — rational, radical, and more.
⏱ longer lecture (skim to the parts you need)

Reading — "The Definition of a Function" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/FunctionDefn.aspx
Why it's assigned: a tight, example-driven page covering the function definition and a solid introduction to domain. A great second pass if the OpenStax page felt long.
⏱ ~8 min

③ Operations on Functions & Composition

Maps to Lecture Segments 5–6. Adding, subtracting, multiplying, and dividing two functions — plus feeding one function's output into another (composition) and why order matters.

Reading — "Composition of Functions" (OpenStax, College Algebra 2e, §3.4)
🔗 https://openstax.org/books/college-algebra-2e/pages/3-4-composition-of-functions
Why it's assigned: covers (f ∘ g)(x) = f(g(x)) with multiple worked examples, the evaluation-at-a-number approach, and the crucial point that f ∘ g ≠ g ∘ f in general.
⏱ ~10 min

Reading — "Combining Functions" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/CombineFunctions.aspx
Why it's assigned: covers all four arithmetic operations on functions with worked examples, then composition — a clean, fast reference for both this week's topics at once.
⏱ ~9 min

Optional one-stop reference (free online)

If you'd like one optional reference to return to all term, Paul's Online Math Notes — Algebra keeps a full, free set of notes online, and Professor Leonard's College Algebra playlist has full-length lectures for every topic in this course.
🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP
Why they're here: reputable, currently-available references you can come back to in later weeks — entirely optional this week.

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §3.1 (functions, notation, evaluating — group ①).
2. Read OpenStax §3.2 (domain and range — group ②).
3. Read OpenStax §3.4 or Paul's Combining Functions (composition — group ③).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes reference above in the meantime.