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April 4th, 2018, 09:28 AM   #1
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Domain of f(x) = 1

Domain of f(x) = 1 is R,

Where is the input(x) being put?

is it in f(x) = 1(x^0) ?

if it is, then we must exclude x = 0 from the domain as 0^0 has no definition.

In this case, domain becomes R - {0}.

I'm confused. Help!
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April 4th, 2018, 09:49 AM   #2
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$f(x)=x^0$ is a different function to $g(x)=1$. It's perfectly acceptable to have a constant function. It returns the same number (1 in this case) regardless of the input. You don't have to "put" $x$ anywhere.
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April 4th, 2018, 09:56 AM   #3
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Quote:
Originally Posted by ThreXys View Post
Domain of f(x) = 1 is R,

Where is the input(x) being put?
It's put into a "black box." Conceptually, the input goes into a machine whose inner workings we have no knowledge of. All we know is that whatever we put in, the number 1 comes out. We can never have any knowledge of what's "inside the function machine." It could be gears and levers, or little elves, or some other process. Of course I'm speaking conceptually. Formally, a function is just a set of ordered pairs. So there's a pair (x, 1) for every real number x.

In fact that's another way we can think about the inner working of the function machine. It's a big lookup table. A number comes in, like 47. The lookup elf goes to the lookup table, finds 47 in the left column, sees that its corresponding output value is 1, and sends 1 out the output chute.

Here's a picture of a function machine.

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April 4th, 2018, 10:26 AM   #4
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The lookup elf goes to the lookup table, finds 47 in the left column, sees that its corresponding output value is 1, and sends 1 out the output chute.
Based on my experience in trying to get the concept of functions across to students, it may be better to refer to one of Maxwell's demons than to elves.

It is my belief that we try to introduce the abstract concept of functions far too early. Students, especially young adolescents, might grasp the concept more easily after they study specific functions and specific families of functions. Abstraction is hard. Generalization without familiarity with specific cases is hard. Mathematics seldom grew historically by developing abstract generalizations before specific instances were known.

Last edited by JeffM1; April 4th, 2018 at 10:29 AM.
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April 4th, 2018, 11:02 AM   #5
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I have a remote for my cable TV. If I punch in 10, I get NBC. If I punch in 49, I get ESPN. I can punch in either 83 or 234 to get the Inspiration network. On the other hand if I punch in 16 and get half the screen PBS and half the screen ABC, then I would say that my remote is not ... wait for it ... FUNCTIONing properly.
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April 4th, 2018, 01:14 PM   #6
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On the other hand if I punch in 16 and get half the screen PBS and half the screen ABC, then I would say that my remote is not ... wait for it ... FUNCTIONing properly.
You are being "pun"ished for your sin. I sentence you to a month with Phil, the ruler of Heck, the Prince of Insufficient Light.

-Dan
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April 4th, 2018, 01:32 PM   #7
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Draw a coordinate axes. Sketch the line y = 1. What is y for any value of x?
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April 7th, 2018, 03:08 PM   #8
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A lot of the problem is due to the ambiguous way the first post if phrased. When I see "f(x)= 1" I immediately think of an equation where f(x) is defined somewhere else and "f(x)= 1" is asserting that there exist a value of x such that "f(x)= 1".

When you want to define a function such that the function value is 1 no matter what x is the, at a minimum say "f(x)= 1 for all x".
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