Homework Help: Calculus

Posted by Anonymous on Tuesday, September 1, 2009 at 8:32pm.

I'm doing graphs/domain/range of basic functions. I have three questions:

How do I find the domain and range of a function? (more preferably range...I'm okay but shaky on domain)
Ex: f(x)=1/(x^2)

Also, how do you write the domain and range with notation? Like when you use symbols like
(-infinity, 0) U (0, infinity)
Specifically, how do I write "All real #'s where x cannot equal..."?

One more thing: what does [[x]] mean? The symbol looks like two brackets very close together or something.

Thank you very much!

Calculus - MathMate, Tuesday, September 1, 2009 at 9:05pm
Domain is the set of valid values as input to the function. In the particular example,
f(x)=1/(x^2)
x can take on all values except ±∞ and 0.
So the domain is (-∞,0)∪(0,+&infin)
which means that the domain can take on all values from (but excluding) -∞ to (but excluding) zero, and from (but excluding) zero to (but excluding +∞.
The range is the interval of possible values when the function is evaluated. In the particular example, the range is (0,+∞). The evaluated function cannot take on negative values as x is squared.

Numerous articles are available for the description of interval notation. Basically, an interval is described by the lower and upper limits, separated by a comma. If the lower limit is included in the interval, a square left bracket is used. If it is to be excluded, a praenthesis (round bracket) is used. The same goes for the upper bound (right bracket.) For example,
[5,+∞) ranges from and including 5 to but excluding infinity.
For more detailed descriptions, see:
http://en.wikipedia.org/wiki/Interval_(mathematics)
http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html
http://en.wikipedia.org/wiki/Domain_of_a_function

I have not come across the [[x]] notation. Please give more information or context of its use.
Calculus - Anonymous, Tuesday, September 1, 2009 at 9:30pm
Thanks for the domain and range info!

Regarding the [[x]] symbol, the function is simply y = [[x]]. There isn't a symbol like that on my calculator (TI-89).

I want to say that this may be the same as brackets, which I believe means absolute value. But what would be the difference between y = lxl and y = [x]?

I'm honestly not sure either...
Calculus - MathMate, Tuesday, September 1, 2009 at 10:06pm
Sorry, I still don't have more information on [[x]]. If you have the answer or someone else has, please post and share the information.

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