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the word function is confusing me. Of course, I have searched and read its definition but i just can not get it. I could just set it in my head but I don't understand it well enough.

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- Thread starter jenniferAOI
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- #1

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the word function is confusing me. Of course, I have searched and read its definition but i just can not get it. I could just set it in my head but I don't understand it well enough.

- #2

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the word function is confusing me. Of course, I have searched and read its definition but i just can not get it. I could just set it in my head but I don't understand it well enough.

A function is a special relation:

A function f: A→B: x→ f(x) is a relation where given an x ∈ A, you can

- #3

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thanks for that. then how about the function which is like a "machine thing"? In what sense exactly?A function is a special relation:

- #4

ProfuselyQuarky

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You mean athanks for that. then how about the function which is like a "machine thing"? In what sense exactly?

- #5

Mark44

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You can think of a function as a sort of machine in which one number goes in (the input), and another comes out (the output). For example if you have a function whose formula is f(x) = 2x - 3, an input value of 5 results in an output value of 7. In function notation, this is f(5) = 2(5) - 3 = 7.thanks for that. then how about the function which is like a "machine thing"? In what sense exactly?

I don't believe she is talking about function composition here.You mean acompositionof functions? Is that what you mean by saying "machine thing"?

- #6

symbolipoint

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I agree fully with you

- #8

Stephen Tashi

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why does a function have to be called function? Can't it be just be called a relation, for instance, of 2 variables?

the word function is confusing me.

It may help to distinguish between "common language" and mathematical terminology. For example, an article on economics might say "job creation is a function of the prime interest rate", which in common language means that the number of jobs created is affected by the prime interest rate. However such a statement wouldn't be interpreted as a claim about a mathematical function - i.e. it wouldn't be a claim that if you are given the exact value of the prime interest rate (e.g. 3.02 %) that you could could determine the exact number of jobs created (e.g. 314,255 ).

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symbolipoint

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- #10

ProfuselyQuarky

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Well said, I really like how you wrote this :)It may help to distinguish between "common language" and mathematical terminology. For example, an article on economics might say "job creation is a function of the prime interest rate", which in common language means that the number of jobs created is affected by the prime interest rate. However such a statement wouldn't be interpreted as a claim about a mathematical function - i.e. it wouldn't be a claim that if you are given the exact value of the prime interest rate (e.g. 3.02 %) that you could could determine the exact number of jobs created (e.g. 314,255 ).

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- #12

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I understand. Is the one we are calling the "function" is theFor example if you have a function whose formula is f(x) = 2x - 3, an input value of 5 results in an output value of 7. In function notation, this is f(5) = 2(5) - 3 = 7.

- #13

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yes and this is where theIt may help to distinguish between "common language" and mathematical terminology. For example, an article on economics might say "job creation is a function of the prime interest rate", which in common language means that the number of jobs created is affected by the prime interest rate. However such a statement wouldn't be interpreted as a claim about a mathematical function - i.e. it wouldn't be a claim that if you are given the exact value of the prime interest rate (e.g. 3.02 %) that you could could determine the exact number of jobs created (e.g. 314,255 ).

comes in.The word "function" relates two things in a special way which applies in both languages. Just that in mathematics, it demands an exact value while in your economics example it was a mere statement of the relationship between the 2 things, right?A function is a special relation

- #14

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thank you. This is a great help.A function being something different than a relation is that a function will give only ONE result for any input. A relation can give more than one result for any one input.

but what kind of reversibility?The distinction is made to help identify possible reversibility.

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In calculus, why does it uses just function and not relation?

- #16

symbolipoint

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thank you. This is a great help.

but what kind of reversibility?

We want to be able to UNDO what a function does.

In calculus, why does it uses just function and not relation?

f(x) can be a function. You put in a number x, and the function gives output y.

We also want some function maybe called g(x), so that g(f(x))=x and f(g(x))=x.

- #17

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okay. So there ain't anyWe want to be able to UNDO what a function does.

f(x) can be a function. You put in a number x, and the function gives output y.

We also want some function maybe called g(x), so that g(f(x))=x and f(g(x))=x.

- #18

symbolipoint

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A function is still a relation; but not every relation is a function.okay. So there ain't anyreversing the processin a relation?

The better way to learn this slow and deep is to study Intermediate Algebra. That will make some ideas clearer.

- #19

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Okay. Thank you. :)A function is still a relation; but not every relation is a function.

The better way to learn this slow and deep is to study Intermediate Algebra. That will make some ideas clearer.

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