Função 01: O que é função?

Matemática no Papel

11 Jul 201804:15

Summary

TLDRThis educational video script introduces the concept of a function in a relatable way. It uses the example of buying gasoline to explain how the price (dependent variable) changes based on the quantity (independent variable) purchased. The instructor demonstrates how a function can represent the relationship between two variables, showing how the cost of gasoline is a function of the quantity bought. The script simplifies the idea of functions by using a multiplication formula to calculate the total price, making it easier for viewers to understand the connection between variables.

Takeaways

📘 The script is a lesson on the concept of a function in mathematics.
🔢 A function is defined as a relationship between two variables, where one variable can change based on the other.
🛒 The example used in the script is the relationship between the quantity of gasoline (in liters) and its price in reais.
💲 It is explained that if you buy double the amount of gasoline, you pay double the price, and similarly for triple the amount.
📊 The price paid is directly proportional to the quantity of gasoline purchased, establishing a linear relationship.
📑 The function is written as a formula where the price (y) is equal to the cost per liter (5 reais) times the quantity (x) of liters.
📈 The script demonstrates how to calculate the price for different quantities of gasoline using the function.
📝 The lesson emphasizes the practical application of functions to solve real-world problems, such as calculating costs.
👨‍🏫 The instructor uses a step-by-step approach to teach the concept, starting with basic definitions and moving to practical examples.
🎓 The lesson is designed to help students understand the concept of functions and how they can be represented mathematically.

Q & A

What is the main topic of the lecture?
-The main topic of the lecture is the concept of a function, specifically exploring how it relates to variables and their values.
What is a function according to the lecture?
-A function is a relationship between two variables, where one variable's value depends on the value of another variable.
What is an example used in the lecture to explain the concept of a function?
-The example used is the relationship between the quantity of liters of gasoline purchased and the price paid, where the price is a multiple of the price per liter.
How does the price of gasoline relate to the quantity purchased in the example?
-In the example, the price of gasoline is directly proportional to the quantity purchased, with the price being a multiple of the price per liter.
What is the price per liter of gasoline mentioned in the lecture?
-The price per liter of gasoline mentioned in the lecture is R$5.
How does the lecture demonstrate the concept of a function with the gasoline example?
-The lecture demonstrates the concept of a function by showing that the total price paid for gasoline is a function of the quantity of liters purchased, calculated as R$5 times the number of liters.
What is the mathematical representation of the function for the gasoline price example?
-The mathematical representation of the function for the gasoline price is P(x) = 5x, where P represents the price and x represents the number of liters.
What is the purpose of using a function to calculate the price of gasoline?
-Using a function to calculate the price of gasoline simplifies the process of determining the total cost for any given quantity, eliminating the need for repetitive addition.
How does the lecture suggest using the function to find the price for a specific quantity of gasoline?
-The lecture suggests using the function by substituting the desired quantity of liters (x) into the function P(x) = 5x to find the corresponding price (P).
What is the total price for eight liters of gasoline according to the function?
-According to the function P(x) = 5x, the total price for eight liters of gasoline would be 5 * 8 = R$40.

Outlines

00:00

📘 Understanding Functions Through a Gasoline Price Example

This paragraph introduces the concept of a function in a mathematical context, using the relationship between the quantity of gasoline purchased and its price as an example. The speaker explains that a function is a relationship between two variables, where one variable (the price) depends on the other (the quantity of gasoline). The example given is a linear relationship where the price is directly proportional to the quantity, with a price of R$5 per liter. The speaker demonstrates how this relationship can be represented as a function, where the total price paid is calculated by multiplying the quantity of liters (x) by the price per liter (R$5). This is a practical way to understand how functions work, as it shows how one quantity can be calculated based on another.

Mindmap

Keywords

💡Function

A function in the context of the video refers to a mathematical concept that describes a relationship between two variables. It is defined as a set of inputs and exactly one output for each input. In the video, the function is used to explain how the price of gasoline depends on the quantity purchased. For example, if the price of one liter of gasoline is R$5, then the function would be represented as 'price = 5 * quantity', where 'quantity' is the input variable and 'price' is the output variable.

💡Variables

Variables are used in the video to represent quantities that can change, such as the quantity of gasoline purchased. The term is fundamental in understanding functions, as functions describe how one variable (the output) changes in response to changes in another variable (the input). In the script, 'x' is used to denote the variable representing the quantity of gasoline, and 'y' represents the price.

💡Price

Price is a key concept in the video, illustrating how it is a function of the quantity of gasoline purchased. The video uses the price as an example of an output variable that depends on the input variable (quantity). The relationship is linear, where the price is directly proportional to the quantity, as shown by the formula 'price = 5 * quantity'.

💡Quantity

Quantity is an input variable in the video's example of a function. It represents the amount of gasoline that a person wishes to purchase. The video explains that the price paid is a function of this quantity, meaning that as the quantity increases, the total price paid also increases, following a linear relationship.

💡Linear Relationship

A linear relationship is a direct proportion between two variables, where a change in one variable results in a proportional change in the other. In the video, the relationship between the quantity of gasoline and its price is described as linear, as doubling the quantity doubles the price, tripling the quantity triples the price, and so on.

💡Input

Input in the context of the video refers to the value that is put into a function to determine the output. The video uses the quantity of gasoline as an example of an input variable. The script explains that the input (quantity) affects the output (price), and understanding this relationship is crucial for grasping the concept of a function.

💡Output

Output is the result produced by a function based on the input. In the video, the price of gasoline is the output, which is determined by the input (quantity). The script uses the example of calculating the total price for different quantities of gasoline to demonstrate how outputs are calculated from inputs in a function.

💡Relation

Relation in the video is used to describe the connection between two variables, where one variable's value is determined by the value of another. The video explains that a function is a specific type of relation where each input has exactly one corresponding output, as seen in the gasoline pricing example.

💡Concept

Concept in the video refers to the fundamental idea or principle being taught, which in this case is the mathematical concept of a function. The video aims to deepen the understanding of what a function is, using the gasoline pricing as a practical example to illustrate the concept.

💡Example

Examples in the video are used to illustrate the concept of a function. The script provides a practical scenario involving the purchase of gasoline, where the price is calculated based on the quantity purchased. This example helps to clarify how functions work in a real-world context, making the abstract mathematical concept more tangible.

Highlights

Introduction to the concept of a function in a tutorial setting.

Function is defined as a relationship between two variables.

Variables are things that can vary by their own nature.

Example given: the relationship between liters of gasoline and price.

Explanation of how price doubles when the quantity doubles.

The price paid is a function of the quantity of liters purchased.

Function can be written to associate price with quantity.

Price is calculated as R$5 times the number of liters.

Function written as 'price equals R$5 times quantity'.

Function simplifies the calculation of the total price for any quantity of liters.

Demonstration of how to use the function to find the price for 8 liters of gasoline.

The function is a practical tool for calculating the cost based on variable quantities.

The concept of a function is fundamental in understanding variable relationships.

The tutorial aims to help viewers understand the logic behind functions.

Invitation for viewers to stay calm and follow along with the tutorial.

Encouragement for viewers to watch the tutorial in sequence for better understanding.

The importance of understanding the foundational logic of functions before moving on.

The tutorial is part of a series that will deepen the concept in subsequent lessons.

The presenter's goal to help viewers grasp the concept of functions by the end of the tutorial.