Better answer to this math problem?

[u/United_Pace2109]

x	f(x)
1.9	0.8
1.99	0.85
1.999	0.9
1.9999	0.95
2.0001	0.95
2.001	0.9
2.01	0.85
2.1	0.8

According to the table, can you infer about f(x)?

The options were lim_{x→2} f(x) = 1, lim_{x→2} f(x) = ∞, lim_{x→10} f(x) = ∞, lim_{x→10} f(x) = 2.

Obviously, the given table matches the function f(x)=0.75-0.05*log10(|2-x|). One of my friends had the same thought process, so they picked the second choice. I knew that the teacher wanted us to choose the first one, so I did.

According to the teacher, the correct answer was the first one, but I feel that it isn't fair that my friend didn't get points. We tried to argue, but she wouldn't give the points.

Is it my friend's problem or the teacher's problem that he lost points on that problem?

[u/soundoftwilight]

The only correct answer is "you cannot infer anything about the limit of this function at 2 from the information provided." This feels like the kind of problem I was shown as a trick in high school to illustrate why graphing out individual values of a function is not an acceptable method to analyze the function. (There are statistical tools which deal with "how do I construct a function given a set of values" but those are both beyond the scope of a class that's teaching about limits and also require you to make assumptions about the shape of the function you expect).

[u/EnvironmentalDot1281 → u/soundoftwilight]

Lovely answer. I want to add that OP’s claim that the values in the table are “obviously” some log function is nonsense.

[u/AdjectiveNounNNNN → u/EnvironmentalDot1281]

There is an obvious simple pattern in the table, and the simplest function that fits that pattern is the one OP stated. In my mind that makes it just as "obvious" as most other underdetermined questions like this.

[u/guti86]

Imho that seems a really bad approach to the subject, limits work with continuous functions, maps of values are like the opposite

[u/BadJimo]

Chose your battles wisely.

It seems that the teacher is unlikely to change her position regardless of arguments/evidence, so probably best to let it go.

If you do pursue a deeper understanding of the question/answer, then just ask what the function f(x) is. You will probably get the response "that was not the question, so it is irrelevant", at which point there is no point continuing the conversation.

[u/Gold_Ad8890]

it's impossible to tell. there are literally uncountably many functions passing through all those points, each with completely different behavior between them.

[u/Bounded_sequencE]

According to the table, can you infer about f(x)?

Nothing.

The function "f" can have any behavior between data points. If the teacher truly believes you can infer otherwise from the data, they should not be teaching.

---

That said, realistically these types of people will likely not be open to mathematical arguments. It is sad that in current day and age, we still have to deal with such BS.

[u/Nanachi1023]

Short answer : None

Limits cannot be inferred through a finite number of points, there is no limit for 10 or 100 or 1000000 points.

Any teacher that is somewhat competent to teach high school math will not consider this a suitable problem.

Just tell your friend he stepped on dog poop, move on.

[u/Varlane]

The second one is the correct answer.

[u/flipwhip3 → u/Varlane]

Obviously other posts are true : you can’t mathematically prove limit here. But extrapolation of the data points seems to imply: every time you add another 9 to the tail of the input it adds 0.5 to the output. This means infinity is a plausible guess

[u/Varlane → u/flipwhip3]

If I'm forced gun to my head to pick an answer, it's 2.

Otherwise, I just mention how bullshit the whole ordeal is.

[u/Temporary_Pie2733 → u/Varlane]

Yeah, it’s growing pretty fast for the limit to be “only” 2, aside from the fact that a simple table will always be ambiguous.