GRADE 9: QUARTER 1

NUMBER AND ALGEBRA

CONTENT STANDARDS:

1. simple geometric concepts and notations.

2. perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal.

INTRODUCTION TO FUNCTION AND RELATION

Relations and functions define a mapping between two sets (Inputs and Outputs) such that they have ordered pairs of the form (Input, Output). Relation and function are very important concepts in algebra and calculus. They are used widely in mathematics as well as in real life. Let us define each of these terms of relation and function to understand their meaning.

DEFINITION OF FUNCTION AND RELATION

Functions and relations are fundamental concepts in mathematics that describe how elements from one set are connected to elements of another. A relation is a set of ordered pairs that show a connection between two quantities. A function is a special type of relation where each input (or domain value) is assigned to exactly one output (or range value). Understanding functions and relations helps us model and analyze real-world situations mathematically.

Note: Please note that all functions are relations but all relations are not functions

Relations - A relation R from a non-empty A to a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
Functions - A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.

Note:

If one value of the domain yields exactly one unique value in the range, then the equation represents a function.
If a rule or an equation represents a function, then it can be written in the form of y = f(x).

Vertical Line Test

This is a test which uses vertical line to check whether the relation expressed in graph is a function or not. If every vertical line intersects the graph not more than once, then the graph represents a function.

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