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The document defines functions and relations, emphasizing that a function relates each domain element to only one range value. It explains key concepts such as ordered pairs, domains, and ranges, along with examples to illustrate the differences between functions and non-functions. The document also highlights a practical tip for identifying functions based on unique x-values in ordered pairs.

FUNCTIONS
Prepared: Sir Ymbhon Gatmaitan

LEARNING COMPETENCIES:
?Distinguishes functions from
relations
?Illustrates functions/relations using
arrow diagram, ordered pairs, table
of values, graphs, equations, and
real-life situations.

FUNCTION:
?A function is defined as a relation where
each element in the domain is related to
ONLY ONE value in the range by some rule.

RELATION:
?It is a rule that relates values from a set of
values (called the domain) to a second set
of values (called the range). A relation is
set of ordered pairs.

ORDERED PAIR:
?An ordered pair is a pair of numbers
written in a particular order,
?(x, y)
Domain/Input Range/Output

EXAMPLE:
A= {(1 ,3), (2, 4), (-1, 0)}
Domain: { 1, 2,-1 }
Range: { 3, 4,0 }

EXAMPLE:
A= {(1 ,2), (3, 5), (-1, 1), (2, 0)}
B= {(3,-1), (4, 2), (3,5 ), (1, 6)}
TIP: Simply look at the value of “x”. If the
elements of the domain are used only once
(no same x-values), then the given set of
ordered pairs is a function.

A= {(1 ,2), (3, 5), (-1, 1), (2, 0)}
B= {(3,-1), (4, 2), (3,5 ), (1, 6)}
Which of the following is a Function?
Function
Not Function

IMPORTANT
CONCEPT
A relation is a function if each x-
coordinate (input) is related or paired to
exactly one y-coordinate (output).
Using a functional notation, a function is
written as f(x)=y

The document explains the distinction between functions and relations, defining a function as a relation in which each domain element is associated with only one range value. It includes examples of ordered pairs, domains, and ranges, illustrating how to determine if a relation is a function based on the uniqueness of x-values. Additionally, it introduces functional notation, expressing a function as f(x)=y.

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The document defines relations and functions. A relation is a set of ordered pairs that relates two sets, called the domain and range. A function is a special type of relation where each element in the domain corresponds to exactly one element in the range. For a set of ordered pairs to be a function, no two pairs can have the same domain value but different range values. Several examples of relations and functions are given.

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The document explains the concepts of relations and functions, including definitions, examples, and ways to express them. It details how to identify the domain and range of relations, differentiate between functions and relations, and includes practical examples and assessments of real-life situations related to these mathematical concepts. The functions are characterized as special relations where each input corresponds to a unique output, with various forms of expression such as set notation, graphs, and equations.

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The document defines relations and functions. A relation is a set of ordered pairs where the domain is the set of first coordinates and the range is the set of second coordinates. A function is a special type of relation where each element in the domain corresponds to exactly one element in the range. Functions can be represented as tables of values, ordered pairs, mappings, graphs or equations. The vertical line test can be used to determine if a graph represents a function - if no vertical line intersects the graph at more than one point, it is a function. Examples are provided to illustrate these concepts.

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This document provides information about relations and functions. It defines relations as sets of ordered pairs and functions as special relations where each element of the domain is paired with exactly one element of the range. It discusses using ordered pairs, tables, graphs and mappings to represent relations. It explains how to determine if a relation is a function using the vertical line test. It also covers functional notation and evaluating functions.

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The document provides information about relations and functions: - It defines key terms like relation, domain, range, ordered pair, and function. - It explains how to represent relations using ordered pairs, tables, graphs, and mappings. - It discusses how to determine if a relation is a function using the vertical line test or by checking if each domain value is mapped to only one range value. - It distinguishes between independent and dependent variables in functional notation.

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This document provides information about relations and functions: - It defines key terms like relation, domain, range, ordered pair, and function. - It shows examples of representing relations using ordered pairs, tables, graphs, and mappings. - It explains how to determine if a relation is a function using the vertical line test or by checking if each element in the domain is paired with exactly one element in the range. - It provides examples of identifying functions from relations represented as ordered pairs, tables, graphs, and mappings. - It introduces function notation and shows examples of evaluating functions. In summary, the document defines relations and functions and provides examples of representing, analyzing, and evaluating them

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Title 狠狠撸 – Exam name and author/date Exam Objectives – Key knowledge domains (administration, monitoring, security) Instance Administration – Managing SQL instances, firewall rules, performance tuning Database-Level Admin – Tables, indexes, triggers, backups Monitoring & High Availability – Query Store, auto tuning, geo-replication Security & Compliance – RBAC, TDE, auditing Tools & Services – Azure Portal, SSMS, Azure Monitor Exam Preparation Tips – Learning paths, mock tests, community support Resources – Official docs, third-party sites, YouTube Q&A 狠狠撸

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1. FUNCTIONS Prepared: Sir Ymbhon Gatmaitan

2. LEARNING COMPETENCIES: ?Distinguishes functions from relations ?Illustrates functions/relations using arrow diagram, ordered pairs, table of values, graphs, equations, and real-life situations.

3. FUNCTION: ?A function is defined as a relation where each element in the domain is related to ONLY ONE value in the range by some rule.

4. RELATION: ?It is a rule that relates values from a set of values (called the domain) to a second set of values (called the range). A relation is set of ordered pairs.

5. ORDERED PAIR: ?An ordered pair is a pair of numbers written in a particular order, ?(x, y) Domain/Input Range/Output

6. EXAMPLE: A= {(1 ,3), (2, 4), (-1, 0)} Domain: { 1, 2,-1 } Range: { 3, 4,0 }

7. FUNCTION: ?A function is defined as a relation where each element in the domain is related to ONLY ONE value in the range by some rule.

8. EXAMPLE: A= {(1 ,2), (3, 5), (-1, 1), (2, 0)} B= {(3,-1), (4, 2), (3,5 ), (1, 6)} TIP: Simply look at the value of “x”. If the elements of the domain are used only once (no same x-values), then the given set of ordered pairs is a function.

9. A= {(1 ,2), (3, 5), (-1, 1), (2, 0)} B= {(3,-1), (4, 2), (3,5 ), (1, 6)} Which of the following is a Function? Function Not Function

10. IMPORTANT CONCEPT A relation is a function if each x- coordinate (input) is related or paired to exactly one y-coordinate (output). Using a functional notation, a function is written as f(x)=y

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