Slight confusion about domain and range + basic functions

GetThroughDiffEq

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Mar 2, 2019
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So, I picked up a teacher's wraparound edition: Advanced Mathematical Concepts - Precalculus with Applications, which seems to be much better at explaining things than my old book. That being said, even after reading the chapter's text, I'm lost on the following questions related to domain and range:

''State the domain and range of each relation. Then state whether the relation is a function. Write yes or no.''

22. {(5, 5), (6, 6)}

For the Domain, I got {(5)} and for the range, {(6)}.

The correct answer is {(5, 6)} for the domain and {(5, 6)} for the range.

I was correct that it was a function.
_____________________________________________________________________________________________________________________________________________________________

''The symbol [x] means the greatest integer not greater than x. If f(x) = [x] + 4, find each value.''

37. f(π)

I got 3.14 + 4 = 7.14.

However, the correct answer is supposed to be 7?

Why?

39. f(q+1)

I got q + 5.

The answer is supposed to be [q] + 5.

Is that correct or would it be marked wrong on a test if I didn't include the brackets?

Thanks in advance.
 

Jomo

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Joined
Dec 30, 2014
Messages
3,351
The domain is the set of 1st values (in red) and the range is the set of 2nd values (in Bold).
{(5, 5), (6, 6)}

You know how to write greatest integer function but you do not seem to understand what it means. You seem to just ignore the brackets! Let [x] represent the greatest integer function. Then, for example, [4.94] equals the greatest integer that 4.94 has obtained which is 4. [9.14] equals the greatest integer obtained which is 9. Note that [14]=14

f(q+1) = [q+1] + 4 = [q] + 1 + 4 = [q] + 5. Yes, you need the brackets!
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,979
''State the domain and range of each relation. Then state whether the relation is a function. Write yes or no.''
22. {(5, 5), (6, 6)}
For the Domain, I got {(5)} and for the range, {(6)}.
The correct answer is {(5, 6)} for the domain and {(5, 6)} for the range.
I was correct that it was a function.
I would have to mark that incorrect because of notation.
Both the domain & range are \(\displaystyle \{5,6\}\).
But yes, it is a function.
____________________________________________________________________________________________________________________________________________________________
''The symbol [x] means the greatest integer not greater than x. If f(x) = [x] + 4, find each value.''
37. f(π) I got 3.14 + 4 = 7.14.
However, the correct answer is supposed to be 7? Why?
\(\displaystyle [x]\) is the greatest integer which does not exceed \(\displaystyle x\).
Because \(\displaystyle \pi\) is not an integer, it means \(\displaystyle [\pi]\ne\pi\), but \(\displaystyle [\pi]=3\).
Thus \(\displaystyle [\pi]+4=7\).
____________________________________________________________________________________________________________________________________________________________
39. f(q+1)
The answer is supposed to be [q] + 5.
Is that correct or would it be marked wrong on a test if I didn't include the brackets?
The expression \(\displaystyle f(q+1)=[q+1]+4\) depends upon what \(\displaystyle q\) equals.
It is true that \(\displaystyle [q+1]=[q]+1\) so \(\displaystyle f([q+1])=[q]+1+4\)
 
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