This problem demonstrates WeBWorK questions where the answer is a list of
numbers
or an interval.
Enter the first three numbers of the form , where is a
positive integer, as a comma separated list.
You could have entered your answer as "1, 4, 9" (without the quotes), or
as "4, 1, 9", or as "2 ^ 2, 1 ^ 2, 3 ^ 2". The order of the
numbers does not matter, and you can still let WeBWorK evaluate expressions
for you.
Now we will enter a few intervals from the real line. WeBWorK can
handle standard interval notation. In each case, we will describe the
set in a couple of ways, and then show you how to enter it. Let's start
with real numbers satisfying . The usual interval notation
for this is .
Enter it just as shown:
Note, you can follow the usual WeBWorK conventions when entering the
numbers in the interval, so you could also enter [ log(100), 2**2 + 1).
Try it. Previewing your answer can help here too if you are having
WeBWorK evaluate your answer.
With intervals, there is a difference between square brackets [] (which mean
to include the end point) and parentheses () (which mean to not include the
end point), and you will need to get them right to have the interval
correct.
If we want to enter an interval where one side is unbounded, such as
the real numbers greater than 3, we would normally write
. Since computer keyboards do not come with an
infinity symbol, we just write out the word infinity .
So, enter (3, infinity).
If we had wanted , we would type -infinity
instead
Finally, sometimes intervals come in more than one piece. For example,
the inequality
is satisfied with and also when .
This would be normally written as the union of two intervals:
To type this into WeBWorK, we just use a capital U for the union symbol:
(-infinity, -5] U [5, infinity)
When using unions of intervals, the order of the smaller intervals does not
matter, so you could also enter [5, infinity) U (-infinity, -5].
Be aware that if you enter intervals which overlap, such as [2, 10)
U (7, 15), WeBWorK will expect you to simplify it into a single interval,
in this case [2, 15).
You can earn partial credit on this problem.