Functions & Inverses – Total Review -Domain, Range, Transformations, GUIDED EXAMPLES Pre‑Calculus

After the lesson take the quiz to check your understanding: https://1drv.ms/w/c/2713457aa143ce7f/... Functions & Inverses – Total Review | Domain, Range, Transformations, Notation (Pre‑Calc 10, 11, 12) and Algebra I, II In this full review lesson from the MathSupport channel, ‪@mathsupportnow‬ , we cover every major concept related to functions and inverses for Grades 10–12 and Pre‑Calculus. You’ll learn what a function is, how to test if a relation is a function, how to write proper function notation, how to determine domain and range, how to perform full function transformations, and how to find the inverse of a function using both algebra and geometric reflection. Perfect for Pre‑Calculus 12 students across Canada, US, UK, NZ, Asia ✅What You’ll Learn in This Video 🔹 1. What Is a Function? Definition of a function Independent vs dependent variables Why each input must have one unique output Examples of linear, quadratic, cubic, reciprocal, exponential, and trig functions 🔹 2. Vertical Line Test How to check if a relation is a function Why graphs that intersect a vertical line twice are not functions Examples of valid and invalid relations 🔹 3. Function Notation 𝑓(𝑥), 𝑔(𝑥), ℎ(𝑥) Rewriting equations using function notation Parent functions and their forms How input/output values behave in notation 🔹 4. Domain & Range How to determine domain (all x‑values) How to determine range (all y‑values) Restrictions from asymptotes, endpoints, and discontinuities Interval notation and set notation Examples with linear, rational, and restricted relations 🔹 5. Function Transformations You’ll learn the full transformation structure: 𝑦 = 𝑎 𝑓(𝑏(𝑥−𝑐))+𝑑 Including: Vertical shifts (d) Horizontal shifts (c) Vertical stretches/compressions (a) Horizontal stretches/compressions (b) Reflections over x‑axis and y‑axis How to apply transformations to points and graphs Step‑by‑step example transforming the point (3, 2) through multiple operations 🔹 6. Inverse Functions What an inverse function represents Why inverses reflect across the line y = x How to interchange x and y How to solve algebraically for the inverse Example: Full example with radicals and squaring both sides to isolate y 00:00 – Introduction 00:08 – What is a function? 00:19 – Vertical line test 01:12 – Function notation 04:14 – Domain and range 07:24 – Vertical & horizontal translations 09:39 – Horizontal shifts 11:02 – Combining transformations 12:00 – Full transformation formula 12:46 – Point transformation example 17:42 – Inverse functions 18:34 – Switching x and y 20:15 – Algebraic inverse example 21:34 – Summary This video is ideal for: 🎯 Pre‑Calculus 12 students 🎯 Grade 10–11 review 🎯 Domain & range practice 🎯 Transformation mastery 🎯 Inverse function preparation 🎯 Exam and quiz review 👍 Like if this helped you 🔔 Subscribe for more MathSupport lessons 💬 Comment with topics you want next 📤 Share with classmates or study groups #functions #inverses #domainandrange #functiontransformations #precalculus12 #verticallinetest #mathsupport