Page 2: Graphical and Algebraic Representations of Functions

This page delves deeper into various representations of functions, focusing on graphical and algebraic methods.

The page presents several ways to describe a function:

1. Graph: A visual representation showing the relationship between x and y values.
2. Table: A systematic arrangement of x and y values in columns.
3. Formula: An algebraic expression defining the relationship between x and y.
4. Graph (again): A more detailed graphical representation on a coordinate plane.
5. Set notation: A mathematical way to express the function as a set of ordered pairs.

Example: The function f(x) = x² - 2 is represented in multiple ways:

• As a table: x = -1, 0, 1, 2, 3 with corresponding y values
• As a formula: f(x) = x² - 2, where x ∈ {-1, 0, 1, 2, 3}
• As a graph on a coordinate plane
• As a set of ordered pairs: {(-1, -1), (0, -2), (1, -1), (2, 2), (3, 7)}

Highlight: The various representations of a function provide different insights into its behavior and properties. Understanding how to interpret and switch between these representations is a crucial skill in mathematics.

The page emphasizes the importance of being able to work with different function representations, as each offers unique advantages in problem-solving and analysis.

Vocabulary:

• Ordered pair: A pair of numbers (x, y) where x is the input and y is the output of a function

This comprehensive overview of function representations equips students with the tools to analyze and describe mathematical relationships in multiple formats, enhancing their problem-solving capabilities in algebra and beyond.