Mathematical Functions and Relationships

Summary:

Functions and relations are mathematical concepts that describe the relationship between two sets of variables. A function is a type of relationship where each value of the independent variable (domain) is associated with exactly one value of the dependent variable (range). On the other hand, a relation is a type of relationship where the independent variable can correspond to more than one value of the dependent variable. Functions can be represented using ordered pairs, equations or graphs, and there are procedures to show that a set of ordered pairs, an equation, or a graph represents a function. To determine whether a relation is a function or not, one can use the vertical line test. The domain of a function is the set of all possible values of the independent variable, while the range is the set of all possible values of the dependent variable. The domain and range of a function can be determined by observing the mathematical expression of the function.

Excerpt:

Mathematical Functions and Relationships

TITLE: FUNCTIONS AND RELATIONS
Learning Competencies:
1. Define Functions and Relations.
2. Differentiate Function and Relation.
3. Explain the different representations of Function. 4. Determine the Domain and Range of a
Function.

A function is a relationship between two sets of variables, x and y, such that each value of set x is associated with exactly one value of set y. The first set of independent variables is the domain, while the second set of dependent variables is the range. For each element of the domain, there corresponds to exactly one member of the range. Therefore, for each value of x, there corresponds exactly one value of y.

A function is used to describe how one variable depends on another. For instance, the amount of money a worker makes is a function of how many hours he works. The number of hours the worker spends on his job is called the independent variable, while the amount of money he makes is called the dependent variable.