Help with Listing Functions w/ Same Range & Diff Domains

AI Thread Summary
Two functions can have the same range but different domains, which is essential for the problem at hand. The functions Y = x/2 and Y = x/2 + 1 both have the same domain and range, which does not meet the requirements of the question. The confusion arises from misunderstanding the definitions of domain and range. A correct example would involve functions with distinct domains while maintaining the same output values. Understanding these concepts is crucial for solving the exercise effectively.
BruceW~
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Homework Statement


question: State two different functions that have same range but different domain. Then tell me what is the range of those two functions.

The attempt at a solution
Y = x/2
Y= x/2 +1

I don't know if that is correct or not. Any suggestion will help.
 
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Missing the relevant expressions! What is the domain of a function ?
And what is the range ?
 
BvU said:
Missing the relevant expressions! What is the domain of a function ?
And what is the range ?
Y = x/2
Y= x/2 +1
Domain will be all real?
Range will be all real too?

This is why I'm confused because they both have all real domain and range, but the question asked two different functions that have same range but different domain
 
What you write is correct, so these two don't help for the exercise !

Let me ask again:
What (in words) is the domain of a function ?
And what is the range of a function ?
 
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BruceW~ said:
Y = x/2
Y= x/2 +1
Domain will be all real?
Range will be all real too?

This is why I'm confused because they both have all real domain and range, but the question asked two different functions that have same range but different domain
Why would that confuse you? You are saying the these functions both have the same domain so they do NOT satisfy the conditions!

So what do you know about "functions", "domains", and "ranges"?

For example, what are the domain and range for "y= 3x for 0< x< 2"?
 
ok, I get it now. Thank you.
HallsofIvy said:
Why would that confuse you? You are saying the these functions both have the same domain so they do NOT satisfy the conditions!

So what do you know about "functions", "domains", and "ranges"?

For example, what are the domain and range for "y= 3x for 0< x< 2"?
 

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