Week 10 · Readings & resources

Week 10 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 10 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 80–95 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (17–20 min total)

① Which way do the ends go? The leading term and end behavior

Chapter 10, Section “Read the far ends from the leading term” · Session 1, Segment 1, “End behavior from the leading term” · Remember: far from the middle, only the leading term matters; its degree and the sign of its coefficient decide both ends.

How Polynomials Behave — Math is Fun — a gentle first look with pictures of the power functions, showing that far from the middle a polynomial looks like its highest-degree term; skip the turning-point count, which this course does not use. (reading, 5–8 min)
Summary of End Behavior or Long Run Behavior of Polynomial Functions — Mathispower4u — a short summary of the four end-behavior cases, sorted by an even or odd degree and a positive or negative leading coefficient. (video, 6 min) (captions: creator)
How To Graph Polynomial Functions Using End Behavior, Multiplicity & Zeros — The Organic Chemistry Tutor — a longer run of sketches that put the ends, the zeros, and the touch-or-cross rule together, one polynomial after another; pause after each one and sketch it yourself first. (video, 20 min) (captions: automatic)

② Cross or touch? Zeros and their multiplicity

Chapter 10, Section “Use multiplicity: cross or touch” · Session 1, Segment 4, “Multiplicity: cross or touch” · Remember: an odd exponent on a factor means the graph crosses the axis there; an even exponent means it touches and turns back.

Tutorial 35: Graphs of Polynomial Functions — Virtual Math Lab — a step-by-step tutorial that finds each zero from its factor, reads the zero's multiplicity from the factor's exponent, and decides whether the graph crosses the x-axis or touches it and turns back there; skip the count of turning points, which this course does not use. This builds on Week 7's work with solving quadratic equations. (reading, 6–9 min)
Find Zeros, Multiplicity, Degree, and End Behavior of a Factored Polynomial (Degree 6) — Mathispower4u — one factored polynomial read from start to finish: its zeros, each multiplicity, the degree as the sum of the exponents, and the ends; use it while working through the Week-10 module overview. (video, 5 min) (captions: creator)

③ Where can the graph not go? Vertical asymptotes and holes

Chapter 10, Section “Find a rational function's domain: vertical asymptotes versus holes” · Session 2, Segment 6, “Vertical asymptotes versus holes” · Remember: factor first; a factor that cancels leaves a hole, and a denominator zero that remains leaves a vertical asymptote.

Tutorial 40: Graphs of Rational Functions — Virtual Math Lab — the vertical-asymptote section factors first, shows a canceled factor leaving no asymptote, and draws each remaining asymptote as a dashed line the graph never touches; skip the slant asymptotes further down, which this course names but does not find. (reading, 5–8 min)
How To Find The Vertical Asymptote of a Function — The Organic Chemistry Tutor — many examples of factoring the denominator first and then telling a vertical asymptote from a hole by whether the factor cancels. (video, 11 min) (captions: automatic)

④ Where does the graph settle? Horizontal asymptotes

Chapter 10, Section “Find the horizontal asymptote by comparing degrees” · Session 2, Segment 7, “Horizontal asymptotes by comparing degrees” · Remember: a smaller top degree gives y = 0, equal degrees give the ratio of the leading coefficients, and a larger top degree gives none.

Graphing Rational Functions, including Asymptotes — Math Hints — the general rules for drawing rational graphs compare the degree on the top with the degree on the bottom, giving y = 0, the ratio of the leading coefficients, or no horizontal asymptote, with many worked examples; skip the long division and the slant asymptotes. Stop here before simplifying rational expressions; next week takes that up. (reading, 8–12 min)
Shortcut for Finding Horizontal Asymptotes of Rational Functions — Patrick J — a quick walk through comparing the degrees of the top and bottom to name the horizontal asymptote, or to see that there is none. (video, 5 min) (captions: creator)
Rational Functions: Finding Zeros, Asymptotes and Sketching the Graph — Patrick J — one rational function sketched from its zeros, its vertical and horizontal asymptotes, and a few test values. (video, 6 min) (captions: automatic)

Optional one-stop reference (free online reference)

Asymptote — Wolfram MathWorld — a mathematics encyclopedia's entry; read the opening definition and the example with vertical and horizontal asymptotes, and skip the asymptotic curves and slanted lines, which go beyond this course. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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