I am doing a Maths qualification at the minute, and am stuck on a tutorial question that involves finding the natural domain of a function, and sketching a graph. Driving me up the wall, as I missed the lecture because of Croke Park hours (a great idea by the way, they really help teaching......). Anyone except OTB and Slimchance (neither of whom I would let walk my dog) think they could help??
The domain of a function is the set of numbers that you can plug into
the function and get out something that makes sense. This is also
called the set of numbers for which this function is defined. In this
case it is the set of all x, such that f(x) is a number.
One way to try to find the domain is to try a couple of numbers just
to get an idea of what might work.
(1) If we plug in 4, we get f(4) = (4+4)/(4^2 - 9) = 8/7.
(2) If we plug in 0, we get f(0) = (4+0)/(0^2 - 9) = 4/-9 = -(4/9)
(3) If we plug in 3, we get f(3) = (4+3)/(9-9) = 7/0 = Oops!
I'm sure you've been told in class that you can't divide by 0, so 7/0
is an answer that doesn't make sense, and one would say that f(x) is
not defined at x = 3. You would find that the same holds for x = -3.
Okay, so far we think that the domain of f(x) is all numbers except
3 and -3. But how do we know this is correct? In principle you would
have to try every real number other than these two to be sure. In
practice it is much easier. You just need to ask yourself a question:
Which is the only way this function can be undefined?
You know that you always get a fraction out of this function. (If you
get a whole number n, you can think of it as the fraction n/1.) The
only fractions that are undefined are those with 0 in their
denominators.
We have a zero in the denominator only when:
x^2 - 9 = 0
or only when
x = 3 or x = -3
This means that the function is undefined only at these two numbers,
so its domain is all real numbers but 3 and -3.
I hope that this has helped. :lol::lol: