مراجعة مجانية ✨ | الحصة الثالثة من دورة المكتسبات في الرياضيات | باك 2026

Introduction

In this tutorial, we will cover the key concepts from the third session of the free mathematics review course aimed at preparing for the Bac 2026. This session focuses on functions, including their definitions, properties, and limit calculations. Whether you are a student or someone looking to strengthen your understanding of mathematical functions, this guide will provide you with clear, actionable steps to master these topics.

Step 1: Understanding Functions

• Definition of a Function: A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.
• Key Characteristics:
  • Each function has a domain (the set of all possible input values).
  • Functions can be classified based on their properties (like being even or odd).

Step 2: Domain of a Function

• Finding the Domain:

  • Identify any restrictions on input values (like division by zero or square roots of negative numbers).
  • Use the following steps:
    1. Write down the function.
    2. Determine any values that make the function undefined.
    3. Specify the valid input range as the domain.

• Example: For the function ( f(x) = \frac{1}{x-2} ), the domain excludes ( x = 2 ). Therefore, the domain is ( x \in (-\infty, 2) \cup (2, \infty) ).

Step 3: Parity of a Function

• Understanding Even and Odd Functions:

  • An even function satisfies ( f(-x) = f(x) ).
  • An odd function satisfies ( f(-x) = -f(x) ).

• How to Determine:

  1. Substitute (-x) into the function.
  2. Compare the result with ( f(x) ) and (-f(x)).

• Example: For ( f(x) = x^2 ):

  • ( f(-x) = (-x)^2 = x^2 ) (even function).

Step 4: Calculating Limits

• Introduction to Limits:

  • A limit helps determine the behavior of a function as it approaches a specific point.

• Steps to Calculate Limits:

  1. Identify the point you are approaching.
  2. Substitute values close to that point into the function.
  3. If direct substitution results in an undefined expression, apply algebraic techniques (like factoring or rationalizing).

• Example: To find ( \lim_{x \to 2} \frac{x^2 - 4}{x - 2} ):

  • Factor the numerator: ( \frac{(x-2)(x+2)}{x-2} ).
  • Cancel ( x-2 ) (valid except at ( x=2 )).
  • Now substitute ( x=2 ) to get the limit as 4.

Conclusion

In this tutorial, we explored the fundamental concepts of functions, including their definitions, domains, parity, and how to calculate limits. These topics are crucial for mastering the mathematics needed for the Bac 2026. To reinforce your understanding, consider practicing with additional exercises and referring to the provided PDF for further examples and explanations. Stay engaged with the content and continue practicing to build a strong mathematical foundation.