Activities 1.7.1 and 1.7.3 #255
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In 1.7.1 it is not possible to determine the value of f(2),
which is okay because the question does not ask for that value.
In part b is asks for f(a) for those "a" where lim_{x\to a} f(x) exists.
That limit does not exist (because the graph wiggles), so the question
does not ask for f(2).
I agree that the hole in the graph at 3 makes it appear the function
is not defined on all of (-4,4). Or maybe the value of f(3) is not in
the range shown in the graph? This could become a feature if
the question also asked: What can you determine about f(3)?
Answer: it is larger than 4 or smaller than -4.
…On Tue, 12 Oct 2021, Mike Shulman wrote:
In these activities, it's not clear to me, or to my students, how one is supposed to deduce the value of
f(2) from the graph. I mean, I suppose the most sensible guess is f(2) = -2.5, since that is the left-hand
limit while the right-hand limit doesn't exist, but that still feels like just a guess. If I were drawing
this graph I would have been inclined to include a large filled dot indicating the value of f(2), like the
ones for f(-2) and f(-1).
Also, while I'm at it, it doesn't seem quite right to say in the preamble to 1.7.1 that this function is
"defined on -4 < x < 4", when in fact it is not defined at 3 (right?).
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However, 1.7.3(b) asks "At which values of a is f(a) not defined", so one must say something about f(2). |
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Sorry that I only addressed 1.7.1.
I agree that 1.7.3 needs some work. In particular, it may be true
that "we were told that f is defined for -4 < x < 4, so that
answers 1.7.3b". But that makes me sound like a lawyer, not a
mathematician. And it is weird to say that f(3) is defined,
but we can't tell whether it is positive or negative.
To slightly change the subject: Maybe if everything on that
page was numbered consecutively, I would have scrolled down to
see Activity 1.7.3, which comes after something else 1.7.3.
…On Wed, 13 Oct 2021, Mike Shulman wrote:
However, 1.7.3(b) asks "At which values of a is f(a) not defined", so one must say something about f(2).
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In general I'm a big fan of consecutive numbering. But here I think it would be a bit confusing for the activities not to be numbered sequentially, since they also appear alone with the same numbers in the activity workbook -- if Activity 1.7.2 were followed by Activity 1.7.4, it would look like something is missing. Perhaps ideal would be to somehow use different numbering schemes for the activities and for other numbered objects like examples, so that the activities would be numbered sequentially and yet there wouldn't be any other 1.7.3 either. I don't have an idea though. |
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Unlike the activity I filed an issue about earlier today, I don't really have any issues with these. To me, activities are not designed to be things written up for homework, but rather are there to provoke thinking and discussion. When a class is ready to notice some of these delicate issues, that's great, and we can chat about them. Other times, I have a class that is not in a position to handle those technicalities, and so we just don't. It doesn't bother me to not get into the weeds on something like that. |
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In general I agree with that approach, but I don't think it's fair to students to ask them to answer a question for which they don't have enough information. If the question were "Do you have enough information to find g(2) and g(3)?" then I wouldn't mind. |
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Mike, all fair points. Thanks for raising them. COVID has derailed my
work on the book for two summers. I will get back, and this is on the
list.
Thanks,
Matt
…On Wed, Oct 13, 2021 at 1:33 PM Mike Shulman ***@***.***> wrote:
In general I agree with that approach, but I don't think it's fair to
students to ask them to answer a question for which they don't have enough
information. If the question were "Do you have enough information to find
g(2) and g(3)?" then I wouldn't mind.
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This appears to have been fixed? |
In these activities, it's not clear to me, or to my students, how one is supposed to deduce the value of f(2) from the graph. I mean, I suppose the most sensible guess is f(2) = -2.5, since that is the left-hand limit while the right-hand limit doesn't exist, but that still feels like just a guess. If I were drawing this graph I would have been inclined to include a large filled dot indicating the value of f(2), like the ones for f(-2) and f(-1).
Also, while I'm at it, it doesn't seem quite right to say in the preamble to 1.7.1 that this function is "defined on -4 < x < 4", when in fact it is not defined at 3 (right?).
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