FUNCTIONS || GRADE 11 GENERAL MATHEMATICS Q1

Introduction

This tutorial covers the key concepts of functions as presented in the Grade 11 General Mathematics curriculum. Understanding functions is crucial for mastering higher-level mathematics, as they are foundational to various mathematical concepts and real-world applications.

Step 1: Understanding Functions

• 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.
• Functions can be represented in multiple ways:
  • Verbal: Describing the function in words.
  • Tabular: Listing input-output pairs in a table.
  • Graphical: Plotting points on a graph.
  • Algebraic: Using an equation to represent the function, e.g., f(x) = 2x + 3.

Practical Tips

• When identifying functions, ensure that each input corresponds to one output. If an input has multiple outputs, it is not a function.

Step 2: Identifying Functions

• To determine if a relation is a function, use the Vertical Line Test:

  • Draw a vertical line through the graph; if it intersects the graph at more than one point, it is not a function.

• Example:

  • The relation defined by {(-1, 2), (0, 3), (1, 4)} is a function because each input corresponds to a single output.

Step 3: Function Notation

• Functions are typically written in the form f(x), where:
  • f indicates the function name.
  • x denotes the input value.
• Example:
  • If f(x) = x^2, then f(2) = 2^2 = 4.

Step 4: Types of Functions

• Linear Functions: Functions that create a straight line when graphed. They can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
• Quadratic Functions: Functions that create a parabola when graphed, typically in the form f(x) = ax^2 + bx + c.

Common Pitfalls

• Confusing linear functions with quadratic functions by misinterpreting their graphs.

Step 5: Operations with Functions

• Addition: (f + g)(x) = f(x) + g(x)
• Subtraction: (f - g)(x) = f(x) - g(x)
• Multiplication: (f * g)(x) = f(x) * g(x)
• Division: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Real-World Applications

• Understanding functions is essential in fields such as economics, engineering, and physics, where relationships between variables are analyzed.

Conclusion

In this tutorial, we explored the fundamentals of functions, including their definition, identification, notation, types, and operations. Mastering these concepts will provide a strong foundation for further studies in mathematics. For next steps, consider practicing with different functions and their graphs to reinforce your understanding.