Funzioni Suriettive & Verifica della Suriettività (Metodo Grafico - Test delle Rette Orizzontali)

Name: Funzioni Suriettive & Verifica della Suriettività (Metodo Grafico - Test delle Rette Orizzontali)
Uploaded: 2025-07-12T00:00:00.000Z
Description: In this video, we'll understand the meaning of a surjective function and how to test for surjectivity using a graphical method called the horizontal line test, which is similar, bu

In this video, we'll understand the meaning of a surjective function and how to test for surjectivity using a graphical method called the horizontal line test, which is similar, but with some differences, to the horizontal line test used to analyze injectivity. You can find this last method here: • Funzioni Iniettive & Verifica dell'Inietti... Alongside this method, there's an analytical method, which we'll cover in one of the next videos. For a full understanding of the aspects covered in this video, I recommend watching the following videos: "Functions - Introduction" ( • Le Funzioni - Introduzione ) "Numeric Functions" ( • Le Funzioni Numeriche ). In this video, we will discuss and discuss the following concepts: Definition of a surjective function (general case) Definition of a surjective numerical function (real functions of a real variable) Definitions of surjective functions in symbolic form Surjectivity through a set-theoretic representation Graphical method for verifying surjectivity (horizontal line test) Surjectivity, or otherwise, of the main elementary algebraic functions This is the outline of this video: 00:00 Introduction 00:27 Definition of a surjective function (general case) 01:07 Definition of a surjective function (numeric functions) 01:38 Recall (Functions, sets, and elements) 01:55 Definition of a surjective function (symbolic form) 02:20 Examples (Set-theoretic Point of View) - Introduction 02:47 Example 1 (Set-theoretic Point of View) 03:14 Example 2 (Set Point of View) 03:35 Example 3 (Set Point of View) 03:54 Example 4 (Set Point of View) 04:17 Example 5 (Set Point of View) 04:42 Horizontal Line Test - Schema 05:45 Horizontal Line Test - Examples (Submission) 06:03 Horizontal Line Test - Example 1 06:48 Horizontal Line Test - Example 2 07:27 Observation (Non-Surjectivity in R) 07:43 Observation (Surjectivity & B) 07:52 Horizontal Line Test - Schema (B = R) 08:00 Horizontal Line Test - Example 3 08:50 Horizontal Line Test - Example 4 09:09 Injectivity, or not, of elementary algebraic functions 09:49 Conclusion 10:07 In the next videos

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