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2.1 - Functions and Relations

2.1 - Functions and Relations

Author: Kyle Webb
Description:

We often form associations between sets of information.  For example, we can form a relationship between month of birth and the names of the individuals in our class.  The associations form some type of rule of correspondence, and in mathematics, these rules are referred to as relations.    

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Tutorial

Difference Ratio

One of the basic definitions in calculus employs the ratio:

fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction

Source: MICDS

Vertical Line Test - Is something a function?

Discrete and Continuous Relations and Functions

A discrete function or relation is one in which the domain can be represented by a finite number of values.  For example, if we consider the relation open curly brackets left parenthesis 2 comma 2 right parenthesis comma left parenthesis 5 comma 1 right parenthesis comma left parenthesis 6 comma 2 right parenthesis comma left parenthesis 9 comma 4 right parenthesis close curly brackets, we see that the graph represents a set of individual points.  This relation can further be classified as a discrete function as it also passes the vertical line test.  

 

A continuous function or relation is one in which the domain contains an infinite number of points and the graph can be represented by a smooth curve or line.  For example, consider the function f left parenthesis x right parenthesis equals 3 x squared minus 1.  The domain consists of all real numbers x, and the graph is shown in the figure below.  

 

 

Source: MICDS