Week 3 · Readings & resources

Week 3 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 3 (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 80–98 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 (17–21 min total)

① Is it a function? One input, one output

Chapter 3, Section “What a function is: one input, one output” · Session 1, Segment 1, “Functions and the vertical line test” · Remember: a function gives each input exactly one output, and a graph passes when no vertical line meets it twice.

Using the Vertical Line Test to Identify Functions — Algebra Class — sets of ordered pairs checked two ways, by asking whether any input has two outputs and by sliding a vertical line across the graph, including a set where two inputs share an output and the relation is still a function; stop here before graphing lines and their slopes, since next week takes that up. (reading, 5–7 min)
The Vertical Line Test — Mathispower4u — a short run of graphs, each checked with a vertical line, so you can practice calling function or not before the answer appears. (video, 6 min) (captions: creator)

② Plugging in: function notation and evaluating

Chapter 3, Section “Function notation: one name, one output” · Session 1, Segment 2, “Evaluating with function notation” · Remember: f(x) is one output, not f times x, and a negative input goes inside parentheses before you square it.

What is a Function — Math is Fun — the gentlest page on this list: inputs, outputs, function names, and why the letter x is only a place-holder; read down through the vertical line test and skip the part on codomains. (reading, 10–14 min)
Function Notation and Evaluating Functions — MathBootCamps — f(x) read as f of x, then functions evaluated at a number, at a negative input kept inside parentheses before it is squared, and at a whole expression such as m + 1, and finally outputs read from a graph. (reading, 6–9 min)
Evaluating Functions - Basic Introduction (Algebra) — The Organic Chemistry Tutor — many evaluation examples in a row, including negative inputs; stop when the video starts solving for a missing x by factoring, which comes later in the course. (video, 12 min) (captions: automatic)
Evaluating Functions (Intro to Function Notation) — Mario's Math Tutoring — four short examples, including a negative input and the whole expression x + h fed into a function; use it while completing the Week-3 module overview. (video, 4 min) (captions: automatic)

③ What goes in, what comes out: domain and range

Chapter 3, Section “Domain: which inputs does the rule accept?” · Session 2, Segment 3, “Domain and range” · Remember: leave out any input that makes a denominator zero or puts a negative number under a square root.

The Domain and Range of Functions — Purplemath — a plain explanation of domain and range for sets of points and for formulas, with a memory trick for telling the two apart. (reading, 8–12 min)
How to find the domain of a function (5 basic examples, rational functions & square root functions) — bprp math basics — the two domain rules from the chapter, worked on rational and square-root functions with every answer written in interval notation. This builds on Week 2's work with writing solution sets in interval notation. (video, 12 min) (captions: automatic)

④ Combining and composing functions

Chapter 3, Section “Composition: the inside goes first” · Session 2, Segment 4, “Combining and composing functions” · Remember: combine two functions output by output at the same input, and in a composition the inside function goes first.

Ex 2: Find Sum, Difference, Product, and Quotient of Functions (Function Arithmetic) — Mathispower4u — four worked examples of adding, subtracting, multiplying, and dividing two functions, each with its domain stated. (video, 7 min) (captions: creator)
Composite Functions — The Organic Chemistry Tutor — evaluating compositions at a number and building them as formulas, working from the inside out. (video, 5 min) (captions: automatic)

Optional one-stop reference (free online reference)

Desmos Graphing Calculator — Desmos — the free graphing calculator this course uses all term; type a rule such as f(x) = 3x^2 - 2x + 5, then f(-2), to check any evaluation, or graph a rule to see its domain and range, and skip the table and regression tools for now. (reading, 5–10 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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