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:
- Graph: A visual representation showing the relationship between x and y values.
- Table: A systematic arrangement of x and y values in columns.
- Formula: An algebraic expression defining the relationship between x and y.
- Graph (again): A more detailed graphical representation on a coordinate plane.
- 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.