In this video we will talk about the importance of functions and their application. We start by reviewing previous concepts such as the relationship, then we define the function and finally we build the graph of some common functions. To finish, we highlight the importance of functions and their application in the modeling of many phenomena and their connection with various areas. The creation of these videos takes me quite a bit of time. If you want to help me continue creating content on YouTube, I invite you to support me on PATREON and ACCESS EXCLUSIVE BENEFITS: / bluedot96 #functions #whatisafunction #functiongraph #differentialcalculus CHAPTERS: 00:00 Introduction 00:35 What is a RELATIONSHIP? 03:20 What is a FUNCTION? 05:48 Real function of real variable 07:25 What is the CORRESPONDENCE RULE of a FUNCTION? 10:34 A FUNCTION IS NOT A MACHINE 13:18 Domain and range of a function 18:32 Graph of FUNCTIONS 18:50 Graph of the function f(x) = x 20:30 Graph of the function f(x) = 2x 21:45 Graph of the function f(x) = x^2 23:24 Graph of the function f(x) = x^3 25:08 Graph of the function f(x) = 1/x 27:10 Why are functions important? 27:59 Thanks and farewell Creating these videos takes me quite a bit of time. If you want to help me continue creating content on YouTube, I invite you to support me on PATREON and ACCESS EXCLUSIVE BENEFITS: / bluedot96 Follow me on Twitter: / bluedot96 Follow me on Facebook: / bluedot1196 Follow me on Instagram: / pauloch96 I RECOMMEND THESE VIDEOS: WHAT IS THE DERIVATIVE?: • The DERIVATIVE changed EVERYTHING ???? WHAT is... WHAT IS THE INTEGRAL?: • What is the INTEGRAL? MEANING of... WHAT IS A FUNCTION?: • A function is NOT A MACHINE WHAT... FUNCTIONS FROM SCRATCH: • WHAT is A FUNCTION? ▶ CART PRODUCT... LINEAR FUNCTION: • What is a LINEAR FUNCTION? ▶ GRAPH... QUADRATIC FUNCTION: • WHAT is a QUADRATIC FUNCTION? ▶ Com... FUNCTIONS OF TWO VARIABLES: • WHAT is A FUNCTION OF TWO VARIABLES?... THE INTEGRAL FROM SCRATCH: • This THEOREM CHANGED EVERYTHING ???? WHAT... DIFFERENTIATION : • This IDEA OF NEWTON FOUNDED the BASIS... RULES OF DERIVATION: • The UNKNOWN side of the DERIVATIVE ????... WHAT IS CALCULUS?: • Why did CALCULUS CHANGED EVERYTHING? ... WHAT IS A LIMIT?: • A FANTASTIC INTRODUCTION to LIMITS... THE LIMIT EXPLAINED IN DETAIL: • WHAT is the LIMIT of a FUNCTION? ▶OF... LIMIT PROPERTIES: • WHAT IS behind the FAMOUS PROPERTIES... WHAT IS OPTIMIZE?: • Why SHOULD YOU LEARN OPTIMIZATION... WHERE DO SIN, COS AND TAN COME FROM?: • REALLY UNDERSTANDING WHAT SIN, COS... UNDERSTANDING SIN, COS AND TAN: • UNDERSTANDING the SIN, COS AND TAN FUNCTIONS You can support the making of more videos of this style by being a MEMBER OF THE CHANNEL, with your help I will be able to make more videos until I complete a playlist with university mathematics from the most basic to the most complex through animations! ************************************************************************************************* The animations in this video were made with Manim (Mathematical animation), a library for Python created by Grant Sanderson (3Blue1Brown). Personally, I find it a very useful tool to better explain many concepts in a visual way. If you are interested, here is the link to the Manim library for Python: https://github.com/3b1b/manim Without further ado, thank you for your attention and see you in the next video