Domain of a function
Irish domain names – Ireland’s domain name
General overview – IEDR
The country code top level domain (ccTLD) for Ireland is .ie. This ccTLD is managed by a not for profit organization in Dublin, Ireland know as the “Irish Domain Registry” or IEDR. The IEDR is not a regulatory body and provides the service to the public and internet community. The registry is responsible for the provision of IE names and the rules relating to their registration. The IEDR implements a dispute resolution policy for domains through the WIPO and unlike other registries operates Monday to Friday during business hours.
Requirements to register
The IE domain itself is a restricted domain in that only applicants who meet certain criteria may register this name. The two main requirements are: Being based in Ireland or having a strong link to Ireland (both northern and southern Ireland). Where the applicant is not based in Ireland information showing this connection must be provided. Secondly the entity registering the domain must have a connection to the name and where this connection is not obvious, must provide evidence of this connection.
Resellers and registration process
Domains are registered through approved domain resellers and are passed to the domain registry directly for approval. The approval process is carried out by a team of people known as IEDR Hostmasters. It is their responsibility to ensure the registration requirements are adhered to. Communication is passed to the approved reseller in the case where more information is required. This thorough process of vetting has led to both positive and negative effects on the domain name’s reputation.
Positive and negative aspects to the domain
On the positive side the domain was recently voted the second safest domain in the world after the Finnish ccTLD. Generally speaking IE domains are held in high regard by Irish based internet surfers. It is seen as a mark of quality or authenticity when doing business online and as a result .ie based websites are trusted over their .com cousins. Very rarely are large spam attacks initiated through an IE domain and the rate of hacks and other internet attacks from IE hostnames is quite low.
The price of .ie domain names are higher than the average TLD or ccTLD, but this price has been significantly reduced over the past 2 years, from an average of around €65 to as low as €19 today. This is due to the traditionally large human input required to approve and manage a domain portfolio. Recently the domain registry themselves have implemented an API mechanism to fast track registration, billing and modifications of domain names. This was carried out by liaising with the reseller community to assess their needs on a day to day basis. Because of the successful implementation of this API amongst the community the price of registering IE domains has fallen with some suppliers leading the way in the price reduction.
Future of the domain
The future of the .ie is bright. New technical advancements in the API as well as the continued reduction in the Irish domain price mean the number of registrations is increasing constantly. Increased promotion of the domain brand by the domain registry and reseller community alike has also led to increased registrations.
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June 22nd, 2009 at 2:57 am
What I would like to know is why this is the first result when you search for ‘funions’ on youtube.
June 22nd, 2009 at 3:09 am
hey thanks….just outta curiosity, do you have a vid like this on finding range or can you direct me 2 a video on this. Thanks!
June 22nd, 2009 at 5:41 am
The last problem was tricky! almost got me
June 22nd, 2009 at 6:04 am
thanks!
June 22nd, 2009 at 2:18 am
1 Domain {10,12,14,16,18} Range {5} Function: yes
2 Domain {18,19} Range{65,66,68,70,72} Function : no
A function has a single value for any member of the Domain – as 2 above has multiple range values for the same domain element then it is not a function.
June 22nd, 2009 at 2:52 am
June 22nd, 2009 at 4:19 pm
in the last example 1/2 is not an even or odd number but it is a real number. Your domain in this example is wrong.
June 22nd, 2009 at 6:27 pm
Forgive me if I’m wrong, but on that last question, isn’t the domain the set of all INTEGERS such that x is not equal to 1?
June 23rd, 2009 at 7:38 am
can you find domain and range of y=2x^2-x? thanks a lot.
June 23rd, 2009 at 3:45 am
2x+18>=0
x>=-9
June 23rd, 2009 at 9:20 am
First factor everything
(x – 2)(x^2 +2x +4)
————————–
(x – 3)(x – 2)
Normally, if you have to find these values, there is no common factor in the top and bottom. You should check with your teacher whether he/she wants you to cancel the x – 2 before you do any of the rest of this.
VERTICAL ASYMPTOTES – what x values would make the bottom zero?
Solve x – 3 = 0 and x – 2 = 0 to find the equations of your vertical asymptotes: x = 3 and x = 2
HORIZONTAL ASYMPTOTES – I assume you are not in calculus . . . so, the only way is to compare the degrees of the top and bottom, then, if the bottom is higher than the top, the H.A. is y = 0, if the degrees are equal, the H.A. is the ratio of the leading coefficients. If the degree of the top is bigger than the bottom, you have no H.A. Instead, you have an angled or oblique asymptote.
Y-INTERCEPT: Set x = 0 and then solve. I assume your question had a 'y =' in front of it. (or f(x))
y = (0-8)/(0-0+6) = -8/6 = -4/3 so the y-int is the point (0, -4/3)
X-INTERCEPT: Set y = 0 and solve. To solve, realize the only way a fraction can equal zero is if the numerator equals zero. So you just need to figure out what makes the top zero. Note that the trinomial factor of a difference of cubes never can equal zero, so for this question you only need to work with the x – 2.
x – 2 = 0
x = 2
So the x intercept is (2, 0).
The DOMAIN of a normal polynomial function is x E R. This means x can be anything real. For a fraction polynomial like this one, the x's in the bottom create 'restrictions' on this domain at any value that would make the bottom zero. So, at your vertical asymptotes, your domain is restricted. For this function, then, your domain is
x is not equal to 2, x is not equal to 3, x E R (Instead of 'not equal to', please use an equal sign with a slash through it.)
June 23rd, 2009 at 9:38 am
Just ask, "What values can the independent variable assume (or not assume)." Is there anything in the function that would 'blow up' if the independent variable assumed a certain value (or range of values). For example
√(x – 1) means x had better be greater than one (at least for you, for now ☺)
1/(x – 1) means x had better never equal 1. Ever.
Look for things like that.
HTH ☺
Doug
June 23rd, 2009 at 10:26 am
The domain is the set of values that you are allowed to use as 'input' for a function. Sometimes the function will refuse some values (for example, SQRT(x) does not allow negative values to be used; 1/x does not allow x=0).
Other times, a domain could be imposed by outside conditions. For example, a function to determine the density of air above a ship, depending on altitude x, should not allow negative altitude — under the ship = water, not air.
Another example, the function that calculates you bank account when you use an ATM should (normally) not allow you to withdraw more money than you have in your account. The domain of x will be limited by your balance.
In your question p is the name of a function. Think of a function as a recipe.
p(x) is the name of the recipe.
x^2 – 2x + 8 is the recipe.
p(5) means: use the recipe and put 5 instead of x
p(5) = 5^2 – 2(5) + 8 = 25 – 10 + 8 = 23
another example (with -17)
p(-17) = (-17)^2 -2(-17) + 8 = 289 +34 + 8 = 331
There does not seem to be any restriction on the domain (meaning: the recipe will work with any x) = the domain of p is from -infinity to +infinity (infinity itself is not included, since it is not a real number).
—
g(x) is a different recipe (g is a different function). A different letter simply warns you that you are now dealing with a different function.
g(x) = 10/(4-5x) will NOT work for any value of x.
If x = 0.8, then (4-5x)=0
g(0.8) = 10/(4 – 5(0.8)) = 10/(4-4) = 10/0
can't divide by zero!
so the value 0.8 is NOT in the domain.
Seems to be the only one that causes the problem, so the domain of g includes all values except x=0.8
June 23rd, 2009 at 7:27 pm
this is scary if u read this this far u will die in 10 days if u dont send to any 15 videos in 2 hours SORRY x .
June 23rd, 2009 at 11:44 pm
Domain of a function is the range of values the independent variable (here x) can take and range of the function is the range by which the values of the dependent variable [here f(x)] is limited.
Q1.
f(x) = x^2 – 9
Here x can take all values from minus infinity to plus infinity.
Hence the domain of the function is from minus infinity to plus infinity.
A squared quantity is always positive. The minimum value of a squared quantity is zero.
So the minimum value of f(x) is -9. It can take maximum values up to plus infinity.
So the range of the function is from -9 to plus infinity.
Q2.
f(x) = |48-x|
Here x can take all values from minus infinity to plus infinity.
Hence the domain of the function is from minus infinity to plus infinity.
The modulus of a quantity is its positive value. It can not be negative. So f(x) can take values from zero to plus infinity.
So the range of the function is from zero to plus infinity.
Q3.
f(x) = 8/(x+9)
Here x can take any value continuously from minus infinity to plus infinity.
Hence the domain of the function is from minus infinity to plus infinity.
f(x) also can have any value from minus infinity to plus infinity.
So the range of the function is from minus infinity to plus infinity.
Q4.
The equation of a straight line is given by y=mx+c where m is the slope and c is the y-intercept.
Here m = 7/3, c= -5
So the linear relation between y and x is
y=(7/3)x -5 or 3y =7x -15.
June 24th, 2009 at 9:34 pm
absolute value?
June 24th, 2009 at 8:38 pm
June 24th, 2009 at 9:56 pm
Usualy there are only two things that youre lookin' for in a domain problem… A problem that has a radical or roots, and a problem with a denominator…
for example, y = square root( 3x-1 ), always for a problem that includes a radical, it radicand, or the number inside the radical should be > or = 0. So equate the radicand to > or = 0.
3x-1>=0
x>=1/3, this is the domain. D = {x|x>=1/3}
for example, y = (2x-1)/(3x-6), the denominator should never be equal to 0. So equate it to 0 , then exclude that number as the domain.
3x-6=0
x=2, the domain is, D= {x | x not=2}
then the rest of domain problems are all real numbers…
hope this helped…Ü