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!
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.
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...
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.
To find the domain and range of a function, let's start with domain. The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of values you can substitute into the function without creating any inconsistencies, such as division by zero or taking the square root of a negative number.
For the given example, f(x) = 1/(x^2), there are no specific restrictions on x, so the domain is usually assumed to be all real numbers. However, it is important to note that x cannot equal 0, as this would result in division by zero. So, the domain in interval notation would be (-∞, 0) U (0, +∞), where the parenthesis indicates that 0 is excluded from the domain.
Now let's move on to range. The range of a function is the set of all possible output values (y-values) that the function can take. In general, to determine the range of a function algebraically, you need to analyze the behavior of the function and identify any limits or asymptotes.
In the case of f(x) = 1/(x^2), notice that the function becomes infinitely large as x approaches 0, both from positive and negative sides. This implies that the range of the function does not include 0 since it is never achieved. However, the function can take all positive values and all negative values (except 0). Therefore, the range in interval notation would be (-∞, 0) U (0, +∞).
To express a domain or range using symbols and notation, you can use interval notation. For example, (-∞, 0) U (0, +∞) means "all real numbers except 0." Just like in the domain example given earlier.
Regarding your last question, the notation [[x]] typically represents the greatest integer function (also known as the floor or integer floor function). It gives the greatest integer smaller than or equal to x. For example, [[3.8]] = 3, and [[-2.3]] = -3.
I hope this helps clarify the concepts of domain, range, notation, and the meaning of [[x]]! Let me know if you have any further questions or need additional explanations.