327 lines
13 KiB
TypeScript
327 lines
13 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
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import { ArrowDown, Check, BookOpen, TrendingUp } from "lucide-react";
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import LinearTransformationWidget from "../../../components/lessons/LinearTransformationWidget";
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import Quiz from "../../../components/lessons/Quiz";
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import { LINEAR_TRANSFORMATIONS_QUIZ_DATA } from "../../../utils/constants";
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interface LessonProps {
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onFinish?: () => void;
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}
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const LinearTransformationsLesson: React.FC<LessonProps> = ({ onFinish }) => {
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const [activeSection, setActiveSection] = useState(0);
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const sectionsRef = useRef<(HTMLElement | null)[]>([]);
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const scrollToSection = (index: number) => {
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setActiveSection(index);
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sectionsRef.current[index]?.scrollIntoView({
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behavior: "smooth",
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block: "start",
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});
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};
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useEffect(() => {
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const observer = new IntersectionObserver(
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(entries) => {
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entries.forEach((entry) => {
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if (entry.isIntersecting) {
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const index = sectionsRef.current.indexOf(
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entry.target as HTMLElement,
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);
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if (index !== -1) setActiveSection(index);
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}
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});
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},
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{ rootMargin: "-20% 0px -60% 0px" },
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);
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sectionsRef.current.forEach((section) => {
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if (section) observer.observe(section);
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});
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return () => observer.disconnect();
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}, []);
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const SectionMarker = ({
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index,
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title,
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icon: Icon,
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}: {
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index: number;
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title: string;
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icon: any;
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}) => {
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const isActive = activeSection === index;
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const isPast = activeSection > index;
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return (
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<button
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onClick={() => scrollToSection(index)}
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className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-blue-100" : "hover:bg-slate-100"}`}
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>
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<div
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className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-blue-600 text-white" : isPast ? "bg-blue-400 text-white" : "bg-slate-200 text-slate-500"}`}
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>
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{isPast ? (
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<Check className="w-4 h-4" />
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) : (
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<Icon className="w-4 h-4" />
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)}
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</div>
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<div className="text-left">
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<p
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className={`text-sm font-bold ${isActive ? "text-blue-900" : "text-slate-600"}`}
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>
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{title}
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</p>
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</div>
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</button>
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);
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};
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return (
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<div className="flex flex-col lg:flex-row min-h-screen">
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<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
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<nav className="space-y-2">
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<SectionMarker
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index={0}
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title="Shift, Reflect & Scale"
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icon={TrendingUp}
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/>
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<SectionMarker index={1} title="Practice" icon={BookOpen} />
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</nav>
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</aside>
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<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
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{/* Section 1 */}
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<section
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ref={(el) => {
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sectionsRef.current[0] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Function Transformations
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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Given a base function f(x), transformations let you shift, flip,
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and scale it predictably. These rules apply to <em>any</em>{" "}
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function type — linear, quadratic, absolute value, or otherwise.
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The SAT tests these with graphs, tables, and algebraic forms, so
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you must recognize them quickly.
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</p>
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</div>
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{/* Transformation Table */}
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<div className="bg-blue-50 border border-blue-200 rounded-2xl p-6 mb-8 space-y-5">
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<h3 className="text-lg font-bold text-blue-900">
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All Six Transformations
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</h3>
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<div className="overflow-x-auto rounded-xl border border-blue-200">
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<table className="w-full text-sm border-collapse">
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<thead>
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<tr className="bg-blue-900 text-white">
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<th className="p-3 text-left">Transformation</th>
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<th className="p-3 text-left">Notation</th>
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<th className="p-3 text-left">Effect on Graph</th>
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<th className="p-3 text-left">Effect on Points</th>
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</tr>
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</thead>
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<tbody className="divide-y divide-blue-100">
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<tr className="bg-white">
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<td className="p-3 font-bold">Shift Up k units</td>
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<td className="p-3 font-mono text-blue-700">f(x) + k</td>
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<td className="p-3 text-slate-600">
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Entire graph moves up by k
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</td>
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<td className="p-3 text-slate-600">(x, y) → (x, y + k)</td>
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</tr>
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<tr className="bg-slate-50">
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<td className="p-3 font-bold">Shift Down k units</td>
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<td className="p-3 font-mono text-blue-700">f(x) − k</td>
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<td className="p-3 text-slate-600">
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Entire graph moves down by k
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</td>
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<td className="p-3 text-slate-600">(x, y) → (x, y − k)</td>
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</tr>
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<tr className="bg-red-50">
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<td className="p-3 font-bold text-red-900">
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Shift Right h units
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</td>
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<td className="p-3 font-mono text-red-700">f(x − h)</td>
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<td className="p-3 text-red-800">Graph moves RIGHT by h</td>
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<td className="p-3 text-red-700">(x, y) → (x + h, y)</td>
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</tr>
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<tr className="bg-red-50">
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<td className="p-3 font-bold text-red-900">
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Shift Left h units
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</td>
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<td className="p-3 font-mono text-red-700">f(x + h)</td>
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<td className="p-3 text-red-800">Graph moves LEFT by h</td>
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<td className="p-3 text-red-700">(x, y) → (x − h, y)</td>
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</tr>
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<tr className="bg-white">
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<td className="p-3 font-bold">Reflect over x-axis</td>
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<td className="p-3 font-mono text-blue-700">−f(x)</td>
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<td className="p-3 text-slate-600">
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Graph flips vertically
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</td>
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<td className="p-3 text-slate-600">(x, y) → (x, −y)</td>
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</tr>
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<tr className="bg-slate-50">
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<td className="p-3 font-bold">Reflect over y-axis</td>
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<td className="p-3 font-mono text-blue-700">f(−x)</td>
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<td className="p-3 text-slate-600">
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Graph flips horizontally
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</td>
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<td className="p-3 text-slate-600">(x, y) → (−x, y)</td>
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</tr>
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</tbody>
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</table>
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</div>
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{/* The #1 Trap */}
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<div className="bg-red-100 border border-red-300 rounded-xl p-5">
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<p className="font-bold text-red-900 text-base mb-2">
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⚠ The #1 Trap — Horizontal Shifts Are BACKWARDS
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</p>
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<p className="text-slate-700 text-sm mb-2">
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f(x − 3) shifts the graph <strong>right 3</strong> (NOT left).
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f(x + 2) shifts the graph <strong>left 2</strong> (NOT right).
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</p>
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<p className="text-slate-600 text-sm">
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Why? Because to get the same y-value, x must be 3 larger. The
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shift in the graph is always <em>opposite</em> to the sign
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inside.
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</p>
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<div className="font-mono text-sm mt-2 bg-white rounded p-2 text-slate-700">
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<p>f(x) = x² has vertex at (0, 0)</p>
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<p>g(x) = (x − 3)² → vertex at (3, 0) → shifted RIGHT 3 ✓</p>
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<p>h(x) = (x + 2)² → vertex at (−2, 0) → shifted LEFT 2 ✓</p>
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</div>
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</div>
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{/* Combined Transformations */}
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<div className="bg-white rounded-xl p-5 border border-blue-100">
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<p className="font-bold text-blue-800 mb-3">
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Combined Transformations — Apply in Order
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</p>
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<p className="text-slate-600 text-sm mb-3">
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When multiple transformations are applied, you can read them
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directly from the equation. Apply in this order: horizontal
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shift → vertical stretch/compress → reflection → vertical shift.
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</p>
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<div className="space-y-3">
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<div className="bg-blue-50 rounded-lg p-4 text-sm">
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<p className="font-semibold text-blue-800 mb-2">
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Example: g(x) = −f(x − 2) + 3
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</p>
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<div className="space-y-1 text-slate-700">
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<div className="flex gap-2">
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<span className="font-bold text-red-600">
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→ shift right 2:
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</span>
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<span>f(x − 2) moves graph right 2</span>
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</div>
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<div className="flex gap-2">
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<span className="font-bold text-purple-600">
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→ reflect over x-axis:
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</span>
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<span>−f(...) flips graph vertically</span>
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</div>
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<div className="flex gap-2">
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<span className="font-bold text-blue-600">
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→ shift up 3:
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</span>
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<span>+ 3 moves graph up 3</span>
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</div>
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<p className="font-mono text-blue-700 font-bold mt-1">
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If f has point (4, 1), then g has point (4 + 2, −1 + 3) =
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(6, 2)
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</p>
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</div>
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</div>
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<div className="bg-blue-50 rounded-lg p-4 text-sm">
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<p className="font-semibold text-blue-800 mb-2">
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Example: h(x) = 2f(x + 1) − 4
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</p>
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<div className="space-y-1 text-slate-700">
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<div className="flex gap-2">
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<span className="font-bold text-red-600">
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→ shift left 1:
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</span>
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<span>f(x + 1) moves graph left 1</span>
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</div>
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<div className="flex gap-2">
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<span className="font-bold text-green-600">
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→ stretch vertically by 2:
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</span>
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<span>all y-values multiply by 2</span>
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</div>
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<div className="flex gap-2">
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<span className="font-bold text-blue-600">
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→ shift down 4:
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</span>
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<span>− 4 moves graph down 4</span>
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</div>
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</div>
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</div>
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</div>
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</div>
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{/* SAT Question Type */}
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<div className="bg-sky-50 border border-sky-200 rounded-xl p-4 text-sm">
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<p className="font-bold text-sky-900 mb-1">
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SAT Question Type: Table of Values
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</p>
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<p className="text-slate-700">
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The SAT may give you a table of values for f(x) and ask for
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values of g(x) = f(x − 2) + 1. Strategy: for each value in the
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g(x) table, work backwards. To find g(3), you need f(3 − 2) + 1
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= f(1) + 1. Look up f(1) in the original table, then add 1.
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</p>
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</div>
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</div>
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<LinearTransformationWidget />
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<button
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onClick={() => scrollToSection(1)}
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className="mt-12 group flex items-center text-blue-600 font-bold hover:text-blue-800 transition-colors"
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>
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Next: Practice Quiz{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 2: Quiz */}
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<section
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ref={(el) => {
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sectionsRef.current[1] = el;
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}}
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className="min-h-screen flex flex-col justify-center"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
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Practice Time
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</h2>
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{LINEAR_TRANSFORMATIONS_QUIZ_DATA.map((quiz, idx) => (
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<div key={quiz.id} className="mb-12">
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<Quiz data={quiz} />
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</div>
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))}
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<div className="p-8 bg-blue-900 rounded-2xl text-white text-center mt-12">
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<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
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<button
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onClick={onFinish}
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className="px-6 py-3 bg-white text-blue-900 font-bold rounded-full hover:bg-blue-50 transition-colors"
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>
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Finish Lesson ✓
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</button>
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</div>
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</section>
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</div>
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</div>
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);
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};
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export default LinearTransformationsLesson;
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