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April 6th, 2017, 01:13 PM   #41
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What about the square root example? In that case the illegal inputs were numbers that put a negative under the square root sign, right? Every problem is different. You have to think about what is a legal input for that problem.
hmm, so a square root can have a zero, but a fraction can't? sorry if i am frustrating.
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April 6th, 2017, 01:25 PM   #42
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hmm, so a square root can have a zero, but a fraction can't? sorry if i am frustrating.
Every problem is different. You have to think about what the legal inputs are to a given function.
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April 6th, 2017, 01:29 PM   #43
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hmm Okay, so how do I know it if I get a zero that it is okay and if I don't get a zero that it is okay?
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April 6th, 2017, 01:33 PM   #44
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hmm Okay, so how do I know it if I get a zero that it is okay and if I don't get a zero that it is okay?
You have to think about it. You have to work with it. If there's a zero in the denominator of a fraction, it's illegal. If there's a negative number under a square root sign, it's illegal.
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April 6th, 2017, 02:04 PM   #45
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You have to think about it. You have to work with it. If there's a zero in the denominator of a fraction, it's illegal. If there's a negative number under a square root sign, it's illegal.
okay thanks for those 2 rules, so if it can be answered should I know how to answer these problems from having solved functions, and problems like these before that had numbers in place for the varibles or is there a name for what I would want to search for to learn how to do this?

Last edited by GIjoefan1976; April 6th, 2017 at 02:14 PM.
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April 6th, 2017, 02:55 PM   #46
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okay thanks for those 2 rules, so if it can be answered should I know how to answer these problems from having solved functions, and problems like these before that had numbers in place for the varibles or is there a name for what I would want to search for to learn how to do this?
Even if they give you a function you've never seen before, you can sit down and ask yourself: What numbers, if I put them into this function, will give me sensible output?

It's like a vending machine. Put in some change, get out a soda. That's what a function is. So if you live in the US and you put American coins into the machine, that's part of the domain because it's a legal input.

If you put Canadian coins or steel washers in the machine, those are not in the domain because they are illegal inputs. Maybe a bad answer since in this case the machine will still do something, it will reject your bogus coins. But you don't get a soda. Mathematical examples are never ambiguous like real life examples.

Here is your step by step procedure.

1. Write down the function clearly, including all parentheses needed to make it unambiguous.

2. Write down a table with two columns. The left column is x, the right column is f(x).

Then you just try all the random numbers you know. 0, 1, and -1 are a good start.

Then you discover for yourself which inputs are legal and which aren't.

In other words just plug in different values till you get a sense of what's a legal input and what isn't.

You investigate the situation. Every math problem is a research problem. Like learning something new. Wow here is this crazy function $\sqrt{x-1}$. I wonder what it does? What happens if I put in $3$? What happens if I put in $-6$? You just experiment around till a lightbulb turns on in your brain, and then it's obvious.

That's the secret sauce. That's how to approach this. Like a murder mystery on tv. You're a detective, investigating the behavior of a function.

Last edited by Maschke; April 6th, 2017 at 03:05 PM.
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April 6th, 2017, 03:07 PM   #47
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Do you have a teacher? Are you in a class?
I do have a teacher and I am in a class but he has in my opinion not taught this yet? and what is sad is this is our first day homework, and we are now onto day 5 of homework it's weird to me as these problems your helping me with are in the fourth section of the first day homework. I have tried to watch youtube videos but I don't seem to find where they show these types of problems, and what makes it even harder is he won't be giving us credit for it all he will only chooses one on the day they are due
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April 6th, 2017, 03:22 PM   #48
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Well you know, I support the work you are putting into understanding this stuff. If you keep at it, it will click. Just like $[1, \infty)$ clicked for you in the $\sqrt{x-1}$ example.

Do you have any tutoring resources available to you? Through the school or outside? Sometimes sitting with someone and having them walk you through this is helpful.
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April 6th, 2017, 03:46 PM   #49
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Thanks I really appreciate that and you. Thanks, Yes thankfully my school offers it but of course the teacher that usually runs it must be sick as everyday this week when I go to the room it is closed and the lights are off Then today I went to someone else and they helped but I showed them the wrong question, and they were very quite as well This why I know I and so Many people are happy for this site, and people like you give sooooo much. As I really do want everyone time to be used for the best. I have been trying to get this done 4 hours everyday.
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April 7th, 2017, 12:34 PM   #50
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Quote:
Originally Posted by Maschke View Post
Even if they give you a function you've never seen before, you can sit down and ask yourself: What numbers, if I put them into this function, will give me sensible output?

It's like a vending machine. Put in some change, get out a soda. That's what a function is. So if you live in the US and you put American coins into the machine, that's part of the domain because it's a legal input.

If you put Canadian coins or steel washers in the machine, those are not in the domain because they are illegal inputs. Maybe a bad answer since in this case the machine will still do something, it will reject your bogus coins. But you don't get a soda. Mathematical examples are never ambiguous like real life examples.

Here is your step by step procedure.

1. Write down the function clearly, including all parentheses needed to make it unambiguous.

2. Write down a table with two columns. The left column is x, the right column is f(x).

Then you just try all the random numbers you know. 0, 1, and -1 are a good start.

Then you discover for yourself which inputs are legal and which aren't.

In other words just plug in different values till you get a sense of what's a legal input and what isn't.

You investigate the situation. Every math problem is a research problem. Like learning something new. Wow here is this crazy function $\sqrt{x-1}$. I wonder what it does? What happens if I put in $3$? What happens if I put in $-6$? You just experiment around till a lightbulb turns on in your brain, and then it's obvious.

That's the secret sauce. That's how to approach this. Like a murder mystery on tv. You're a detective, investigating the behavior of a function.
Okay that helps that I should still be able to solve a problem even if it looks different and thanks for the column information.
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