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.

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MathematicsFunctionsEducationTutorialPrice-QuantityCalculationVariablesRelationTeachingLogic
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