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:
- Verbal description
- Graph
- Table
- Formula
- Set notation
Example: The function fx = x² is shown, mapping values like f−1 = 1, f0 = 0, and f1 = 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
