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.

Page 1: Introduction to Functions and Their Representations

This page introduces the concept of functions and various methods to describe them. It emphasizes that a function assigns each element from one set (domain) to exactly one element in another set (codomain).

Definition: A function is a relationship that assigns each element of a set X (domain) to exactly one element of a set Y (codomain).

The page illustrates this concept with examples, showing how elements from set X are mapped to elements in set Y. It also introduces different ways to represent functions:

1. Verbal description
2. Graph
3. Table
4. Formula
5. Set notation

Example: The function f$x$ = x² is shown, mapping values like f$-1$ = 1, f(0) = 0, and f(1) = 1.

Highlight: It's important to note that while each element in the domain can only be assigned to one element in the codomain, multiple elements in the domain can be assigned to the same element in the codomain.

The page concludes with an example of a verbal description of a function: "The function f assigns to each number in the set the square of that number multiplied by 2."

Vocabulary:

• Domain: The set of input values for a function
• Codomain: The set of possible output values for a function