Graphical Representation of Functions

This page demonstrates the practical application of graphical function representation using a coordinate system. The visualization shows how functions can be plotted on a two-dimensional plane.

Highlight: The coordinate system consists of:

• X-axis (horizontal): represents antecedents
• Y-axis (vertical): represents images

Example: The graph shows multiple points plotted across the coordinate system, demonstrating the relationship between antecedents and their corresponding images.

The page includes a detailed grid system extending from -2 to 22 on the x-axis and -6 to 17 on the y-axis, allowing for precise plotting of function values.

Understanding Mathematical Functions - Basic Concepts

This page introduces the fundamental concepts of mathematical functions and their various representations. The content focuses on the definition of functions and their key components.

Definition: A function is a process that associates a unique number f$x$ with each input number x.

Vocabulary:

• x: antecedent (input value)
• f$x$: image (output value)
• f: function name

Example: In numerical notation:

• f(3) represents the image of 3 through function f
• If x is an antecedent, f$x$ is its image through function f

Highlight: A key principle is that while one antecedent can only have one image, a single image can have multiple antecedents.

The page also outlines three methods for determining functions:

1. Through value tables
2. Through algebraic expressions $e.g., f(x)=3(x-1)²$
3. Through graphical representation, with antecedents on the x-axis and images on the y-axis