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Domain are the values of x allowed in the function Range are the values of y outputted by the function So for the domain what values of x correspond to the function? What values of y correspond to the function? Hint this function clearly has asymptotes
I am still really confused on how i would find the values that x corresponds with
Anyone who can help?
Are you familiar with set notation?
A function by definition passes the vertical test (you can draw a straight vertical line through the function and not intersect it more than once) and is essentially made up of an input variable, usually designated as "x" and an output variable usually designated as "y" although a lot of the time the notation f(x) is used to designate "y" (but I wont get into that unless you want me to) some functions: y = x^2 y = x + 2 etc. This is not a function because it doesn't pass the vertical line test, y^2 = -x^2 it is a circle :\ A graph of a function is essentially all the input and output values possible drawn out
So with the basic definition out of the way you should notice right away with some functions you cannot put certain values into x and get out a y for example, y = 1/x you should notice right away if we set the input variable, x=0 we have a problem, y = 1/0 You cannot divide by zero, it gives us an undefined output value. So we can say that 0 in this case is not in the domain of the function, because the domain is just the values of x that can be plugged in a function to give a value y we can denote that by using set notation (-infinity, 0),(0,+infinity) round brackets basically mean that the function can have values plugged into it that go infinitely close to the number that cant be plugged in (you can plug in 0.000000000000000000000001 because it isn't zero), you always use round brackets with infinities square brackets are used when the number is included in the function but stops after for example, y = x^(1/2) its domain would be, [0, +infinity) you cant take the square root of a negative number, but you can take the square root of zero Note: some teachers request different notations so you might want to consult with them but this is what is normally used from my experience. The range is essentially similar to the domain the only difference is it is concerned with allowed output values
sorry I made a mistake, x^2 = y^2 is a plane not a circle
If you have any questions please feel free to ask
This link defines pretty well what a relation is and how a function is just a special kind of relation, http://answers.yahoo.com/question/index?qid=20070927082420AAqNPyy
I know this seems like a lot to read but if you understand this stuff you will be better off