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Chapter 4 - Functions

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Function Definition


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Functions - Function Definition - Contents

A mathematical function is an equation that assigns a single answer to each possible question. A variable represents an unknown value in the function's equation. The function's input variable is usually represented by an x. This is the independent variable to the function. The function's output is a variable usually represented by y. This is the dependent output of the function. To be a function every x value has to have one and only one answering y value. More than one x value can yield the same y value as long as there is the only one answering value. Function mapping of a mathematical equation with two variables takes the elements of the domain set and maps them onto the function's range set on a two-dimensional grid. This grid is called a Cartesian Plane named after the French Renaissance mathematician Descartes. The grid has bisecting perpendicular coordinate number lines each representing the set of real numbers intersecting at the zero point of both number lines at the center of the grid. This is the origin of the Cartesian Plane Using this coordinate system a function's variables are assigned x and y values which can be mapped out as a two-dimensional representation. A map of a function can be continuous or discontinuous. This can be shown by mapping the function on to the Cartesian Plane to see if it is a continuous line. Continuity of a function can also be mathematically proved by examining summations and limits of the function. There are a series of fundamental mathematical functions used in basic math, geometry and trigonometry that will be examined in the following chapters.

Functions - Function Definition - Examples

Function mapping:
From the function
y = x squared,
(x
, y) = (1, 1), (2, 4), (3, 9) . . .

Functions - Sections - Chapters
1 - Function Definition 2 - Function Notation 3 - Function Domain
4 - Function Range 5 - Composite Functions 6 - Inverse Functions
7 - Linear Functions 8 - Power Functions 9 - Quadratic Functions
10 - Logarithmic Functions 11 - Exponential Functions 12 - Factorial Functions
13 - Limit Functions 14 - Summation Functions 15 - Percentage Functions

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