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These are applied in our everyday life! Not to mention in Physics, Engineering, Economics, Social Sciences, etc.

A very simple example. Suppose 1 gallon of a certain fuel you need costs 3 US$. So, there's a function that, to each volume V of this fuel, assigns the cost C in which you incur to by this volume. This function is given by C = 3 V. So, when you want to know how much you'll pay if you want the volume V, then you implicitly, probably even without realizing, you compute the value of this function. And also, again probably without realizing, you know this function is a bijection, that is, to each V there corresponds only one C and different values of V lead to different values of C.

Now suppose you have C dollars and you want to know how much fuel you can buy with these C dollars. Then you do a kind of inverse thinking, you compute V = C/3. What did you do, without realizing, or at least without thinking about? You determined the inverse of the function C = 3V. Computing V = C/3, you implicitly worked with the inverse of the previous function, that is, the function that, to each amount of money C, gives the amount V of fuel you can buy.

Isn't this a good reason to study functions and their inverses?

Q: What is the importance of classifying function and relation?

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Not every relation is a function. But every function is a relation. Function is just a part of relation.

A function is a relation whose mapping is a bijection.

No. A relation is not a special type of function.

Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.

A relation has pairs of numbers. A function is a special relation where for each input there is one and only one output.

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Science. The importance of vitamins to the body, blood, skin, eyesight, metabolism, reproduction require a vitamin. Some compliment another to function. Function may involve mutual inclusion or exclusion of other functions. Choosing a role for usage. $!

Not every relation is a function. But every function is a relation. Function is just a part of relation.

The importance of classifying animals into groups is to have things well organized so that it will not be too complicated.If we do not classify them,we will get mixed up. :):)

No, a function must be a relation although a relation need not be a functions.

Does the graph above show a relation, a function, both a relation and a function, or neither a relation nor a function?

Not every relation is a function. A function is type of relation in which every element of its domain maps to only one element in the range. However, every function is a relation.

yes.

A function is a relation whose mapping is a bijection.

No. A relation is not a special type of function.

A relation is a function if every input has a distinct output.

Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.

describe energy balance and its importance in relation to sports performance