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Explore the fundamental concepts of functions in mathematics, including their definition as unique associations between sets, and their essential characteristics like domain and range. Functions are depicted through various graphical forms, such as lines for linear functions and parabolas for quadratic functions. The text delves into function evaluation, graphical interpretation, and advanced functions like exponential and logarithmic types.

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## Definition of Functions

### Relation between sets

Functions are mathematical rules that uniquely associate elements of one set with elements of another set

### Function notation

Symbols used in function notation

Function notation uses symbols like f(x) to represent the name and variable of a function

Evaluating functions

To evaluate a function, substitute a value for the variable and perform the prescribed operations

### Domain and range

The domain is the set of allowable inputs, while the range is the set of all possible outputs for a function

## Graphical Representations

### Function diagrams

Function diagrams visually show the relationship between inputs and outputs

### Graphing functions

Plotting points

To graph a function, plot points corresponding to input and output values and connect them to show the function's behavior

Types of functions and their graphs

Different types of functions, such as linear, quadratic, and trigonometric, have characteristic graphical forms

### Vertical line test

The vertical line test is a graphical technique used to determine if a curve represents a function

## Characteristics of Functions

### Domain and range

The domain of a function is the set of all input values for which the function is defined, while the range is the set of all output values it can produce

### Types of functions

Basic types of functions

Linear, quadratic, and trigonometric functions are common types of functions with characteristic graphical forms

Complex functions

Functions can also be more complex, such as higher-degree polynomials, exponential, and logarithmic functions

Algorino

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