Week 10 — Readings & Resources · Polynomial & Rational Functions

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 7 — Analyze polynomial and rational functions using end behavior, zeros and multiplicity, domain, and vertical and horizontal asymptotes.

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: ~4 short readings + ~2 videos, grouped by the lecture's four ideas. 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 50–65 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① polynomial end behavior → ② zeros and multiplicity → ③ rational-function domain & vertical asymptotes → ④ horizontal asymptotes.

A habit to keep sharp: the AI tutorial this week ends by having you catch a chatbot's mistake on horizontal asymptotes. Keep that posture as you read — the tool drafts, you check.

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 in the optional section as a backup.

① Polynomial End Behavior & Zeros

Maps to Lecture Segments 2–3. The leading term tells you the shape of both tails; the factored form tells you where the graph crosses or touches the x-axis.

Reading — "Power Functions and Polynomial Functions" (OpenStax, College Algebra 2e, §5.2)
🔗 https://openstax.org/books/college-algebra-2e/pages/5-2-power-functions-and-polynomial-functions
Why it's assigned: covers end behavior from the leading term (even/odd degree, sign of the leading coefficient), zeros, and how multiplicity governs whether the graph crosses or touches. Worked examples match the lecture examples closely.
⏱ ~10 min

Reading — "Graphing Polynomials" (Paul's Online Math Notes — Algebra, §5.3)
🔗 https://tutorial.math.lamar.edu/Classes/Alg/GraphingPolynomials.aspx
Why it's assigned: a tight, example-driven walkthrough of end behavior, zeros, and the touch-vs.-cross multiplicity rule — exactly the two ideas that carry the most quiz weight this week. Great second-pass resource if the OpenStax examples feel dense.
⏱ ~8 min

② Rational Functions: Domain, Vertical Asymptotes & Horizontal Asymptotes

Maps to Lecture Segments 5–6. Factor the denominator for domain and vertical asymptotes; compare degrees for the horizontal asymptote.

Reading — "Rational Functions" (OpenStax, College Algebra 2e, §5.6)
🔗 https://openstax.org/books/college-algebra-2e/pages/5-6-rational-functions
Why it's assigned: the most complete treatment of all three rational-function tools in one place — domain, vertical asymptotes (with the hole distinction), and all three horizontal-asymptote cases, with clearly worked examples. Start here.
⏱ ~12 min

Reading — "Graphing Rational Functions" (Paul's Online Math Notes — Algebra, §4.8)
🔗 https://tutorial.math.lamar.edu/Classes/Alg/GraphRationalFcns.aspx
Why it's assigned: walks through the six-step sketch strategy from the lecture — factor, find excluded values, determine asymptotes, find intercepts, check behavior. A practical complement to the OpenStax theoretical treatment.
⏱ ~10 min

③ Video: Polynomial Graphs & Rational Functions

Maps to the lecture's worked examples. Watch to see the end-behavior tails, the touch-vs.-cross at zeros, and the asymptotes drawn live.

Video — "How to Sketch Polynomial Functions" (Professor Leonard — Precalculus/College Algebra 31)
🔗 https://www.youtube.com/watch?v=6MAtqY6Fqjs
Why it earns the click: an unhurried, full-length walkthrough of end behavior, zeros, and the touch-vs.-cross multiplicity rule, with every step shown at the board — the same six-step sketch strategy from the lecture.
⏱ longer lecture (skim to end behavior and multiplicity sections)

Video — "Discontinuities of Rational Functions" (Khan Academy)
🔗 https://www.youtube.com/watch?v=qoMimDT7D8w
Why it earns the click: short, focused coverage of vertical asymptotes and holes — exactly the distinction that trips students up — with a graphical walkthrough showing how a canceling factor becomes a hole rather than an asymptote.
⏱ ~7 min

Optional one-stop reference (free online)

If you'd like one optional reference to return to throughout the rational-functions arc (Weeks 10–12), Paul's Online Math Notes — Algebra keeps a full, free set of notes, 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 return to in Weeks 11 and 12 as well — 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 §5.2 — end behavior and multiplicity (group ①).
2. Read OpenStax §5.6 — domain, vertical asymptotes, horizontal asymptotes (group ②).
3. Watch the Khan Academy video on rational function discontinuities (group ③).