How do i get the Domain and Range? if I dont have the information.
Imagine that our Math 107 class goes down to the Pierces track and each person is timed running one lap around the 400-meter track.
The function T(n) gives the time T as a function of the person’s name n. (So input name, output time.)
Is this actually a function?
Domain:
Range

- anonymous

- katieb

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- amistre64

the domain is all the input values that are allowed; the range is all the outputs values that could happen as a result.

- amistre64

a function takes one input and produces one output.... so if each person is an input, then there output is only one number...their time. so yes, it is a function

- amistre64

does that make sense?

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- anonymous

should I be making some type of chart, how to I write the domain and range

- amistre64

in this case, you can make a chart if you want.. or you can draw 2 circles. one circle is named "domain" and the other circle is named "range".
The domain of the funtion is equal to "each person that ran the track".
the range of the function is equal to "the time it took them to finish one lap".
If you can match up each element of the domain with one and ONLY ONE element inthe range, then you have the definition of a function.
for example:
Domain, Range:
Bob, 5 min
Gary, 7 min
Lisa, 3 min
Henry, 7 min
Flo, 6 min
etc....

- anonymous

O, Ok I understand. I have another domain and range problem that includes a graph and Im pretty confused it has to points and two different lines could you help?

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- amistre64

could I help? maybe :)

- amistre64

yeah, it looks like I can help with that...

- amistre64

in order for this to be defined as a "function" we need to see that for every value of "X" there is one and ONLY ONE value for "Y". One way to test for that is called the "vertical line test".. I know.... not a very exciting name, but descriptive nonetheless.
we draw line that go from top to bottom and if they only touch the graph in one spot, then its a function.... make sense?

- anonymous

It does make sense.

- amistre64

The "domain" is any value of "X" that actually produces a number value for "Y". If there is no value for "Y" for any given value of "X" then that "X" value is not included in the domain...
for example, we see in this graph that when x = 1 there is no value for "y". therefore x is not in the domain... does that make sense?

- anonymous

That makes sense

- amistre64

good, now lets see if you can tell me what you believe the "domain" of this function would be..... right or wrong, give me your best guess :) remember, any value of "x" that gives us a "y" value is IN the domain....

- anonymous

-1,2

- amistre64

very good, we see that there are spots on the graph that have been marked. There are also "arrows" on the ends of the graph to tell us something.
Lets start with those "dots" tho. When we have a solid dot, it means that that value is INCLUDED. But, when we have an "open" dot, a little circle, that tells us that we get close to this number, but can never reach it, so we do not keep it in our domain....does that make sense?

- anonymous

that make sense

- amistre64

good....youre a smart one :)
The "notation" we use for those dots are:
() means it gets close to, but never equals the value; and is therefore not part of the domain.
[] means that it does equal and is part of the domain.
(-1), [2] is what we have so far....right?

- anonymous

That is right.

- amistre64

good...
now we need to fill in more of this domain...lets notice if there are any "arrows" at the ends of our curve of the graph.
an "arrow" tells us that this curve continues on and on and on and on for ever and ever.... towards "infinity".
The thing about "infinity" is that it is one of those values that can be gotten near to , but never reached....so we always use () when infinity is involved...
we have a -infinity and a +infinity involved with our graph right?

- anonymous

That is correct one arrow is going to the left and one is going to the right.

- amistre64

then we can fill in more information about our domain:
(-infinity, -1) [2, infinity) now this is good, but there is one more thing we need to do to finish this domain up.... we need to tell people what to do with the "x" values that are missing between -1 and 2.
We can use symbols or words.... the symbol for "and" looks like an upside down "U"; and the symbol for "or" looks like a normal "U". but I will use words instead...just easier to type :)
We define "and" to mean: all values that are in common.
{1,2,3,4,5} and {1,5} means: that the only values we can use are 1 AND 5, because that is the only values they have IN COMMON.
when we want to use any value contained in our "sets", we use the word OR.
{1,2,3,4,5} OR {3,4,5,6,7} means that we use ANY value that is given to use: 1,2,3,4,5,6,7 are all good to use.
the word we will use to finish our domain is "OR"...like this:
(-inf, -1) OR [2, inf) does that make sense?

- anonymous

that does make sense

- amistre64

very good.
Since our domain is finished, lets use the same notation for finding out our "range". The range of this function is the lowest and the highest values that we can get out of it.
What do you see as the lowest value of "y" and the highest value of "y"?

- anonymous

-3,8

- amistre64

excellent...
and since -3 has a "circle" and not a "dot" we use () for it...
8 looks like it is actually reached so we will use [] for it, like this:
range = (-3,8]

- anonymous

that seems to be correct

- amistre64

then we are finished with the problem :)
Domain: (-inf, -1) OR [2, inf)
Range: (-3, 8]
thats it :)

- anonymous

Thank you very much!

- amistre64

youre welcome :) keep practicing..

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