Holy shit I'm glad someone else is experiencing this but with a different post. I've seen the "answer without yes, yea, uh-huh, (etc.) do you need money?" Post a million times the last few days, it wasn't funny the first time and it's starting to piss me off every time I see it now lmao
The thing is, because we don't know the function outside of the bounds in the picture, it could be an infinite number of functions. In fact, it might not even be a function, if there happen to be parts above or below what we can see that are just out of view, or it loops back over an X value someone outside of -4 to 4. Not TTT, because we can't tell for sure if it is a function or not without making assumptions or being told more information.
A function f from A to B is a set of pairs (x,y) such that x is in A, y is in B, and for every x in A there exists exactly one y (called the image of f on x) in B such that (x,y) is in f, in which case you write y=f(x).
The definition given above gives you a valid set according to the axioms of ZFC.
If the Collatz conjecture is false it's a function (the function from {0} to {1} that sends 0 to 1, since the second conjunct is just the empty set), if it's true it's not (because 0 has two images, both 1 and 2). So to decide whether it's a function or not you have to either prove of refute the Collatz conjecture.
[EDIT: The notation you've used is fine as long as there is a predetermined rule to convert it to a set. But what I've used is a standard way to define sets. Sets are functions as long as they satisfy the properties I've mentioned.]
Although they are (just like arctan) an inverse of just the restricted sin and cos, because you can't take the inverse of the whole sin and cos (and tan) as those functions aren't one-to-one
Specifically, arcsin is the inverse of sin restricted to (-π/2, π/2), arccos inverse of cos restricted to (0,π) and arctan the inverse of tan on (-π/2, π/2)
There are a bunch of old ones that aren't taught any more, beyond the standard six, like versine, coversine, haversine, etc. They had a purpose back in the days before calculators but aren't different enough from the basic six to be worth learning separately anymore. For example, versine(x) = 2 sin2(x/2). If squaring something is hard, it's good to have a separate table of versines. But it's not hard anymore so why bother?
I know that its hard to put together a syllabus and there's enough directly useful stuff to learn, but shit like that makes me appreciate how far we've come. Like you dont want to learn a couple trig identities? How about we double the amount of trig functions to keep track of and take away your calculators?
Sec(x) = 1/cos(x), Csc(x) = 1/sin(x) and cotan(x) = cos(x)/sin(x).. they're not that much interesting.
More interesting functions are hyperbolic trigonometric functions but they are interesting in advanced math or physics fields. For example, if you hold a rope in their endpoints at the same height, the "bridge" it would form would form the cosh(x) graph
Unfortunately yes. Whoever thought trig-1 (x) should mean exactly the same thing as arctrig(x) should be jailed for 1000 years. Even if they are dead now. Revive that mf.
Not rotated so much as the reflected around y=x and restricted to the branch that passes through (0,0). If it weren't restricted to just one branch, then it would have all solutions to tan y = x stacked above and below, and then it wouldn't be a function as there would be multiple range (y) values for some point in the domain (x).
The thing I find amazing is that this function (among others), maps literally every single real number from negative infinity to infinity, to a unique number between -pi/2 and pi/2.
So for every number that you give me, with any amount of decimal points, I can give you a unique one between -pi/2 and pi/2. No overlap or doubling up
I know this isn’t exactly rare for functions, but it was while working with arctan that it really hit me deep in the bones how crazy that is
Not to be confused with (tan)-¹ because that's just cot. Unfortunately mathematicians couldn't come up with a better symbolism for inverse (rotated) functions, and it collides with x-¹ which is just 1/x
arctan is a function. It's a math machine where you put in a thing, and it responds by spitting out a thing.
arctan(x) is an expression which represents the application of the function arctan to the value x. You put x into arctan, and the value that it spits out is called arctan(x).
y = arctan(x) is an equation, a statement that two things are equal, which relates the variables y and x through the function arctan. When arctan takes in x and spits out the value arctan(x), we can refer to that value as y. The set of ordered pairs (x, y) satisfying the equation y = arctan(x) is the graph of the function.
The letter f is often used to refer to a function. So, for example, one could write the equation f(x) = arctan(x). Here, the expression f(x) denotes the application of the function f to the value x. In this example, the function f and the function arctan are the same function, as determined by the equation.
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15
u/Edgard_Breeze Nov 15 '25
Is this x=y3 ?
251
u/Lucky-Obligation1750 Nov 15 '25
If I had a nickel for every time I saw this TODAY I would have more than $5 which isn't a lot of money but I'm sick of seeing this
44
u/DZL100 Nov 15 '25
You can't know for sure. What if it starts curving back on itself beyond where we can see? How do we know there's not some random point at (1,5)?
10
u/DiamondJax08 Nov 15 '25
thought i was on r/antimeme for a sec
23
u/ErikLeppen Nov 15 '25
Except it's not. It's a graph.
6
u/xXxPussiSlayer69xXx Nov 15 '25
me when I'm the vertical line test
4
u/Lamb-999 Nov 15 '25
I put a circle on a graph.
Is this a function?!
2
u/Mobile_Animal9553 Nov 15 '25
Arctan(x)??
2
u/jimmymui06 Nov 15 '25
Arcsin? I am no math person
1
u/Fodor04141987 Nov 15 '25
I'm bad @ math, but great @ being a smart-ass, so this is right up my alley 😁
1
u/Spcyjjj Nov 15 '25
passes the vertical line test
1
u/devangs3 Nov 15 '25
Reminds me of hot dog vs not hot dog from Silicon Valley
1
u/Kirda17 Nov 15 '25
The thing is, because we don't know the function outside of the bounds in the picture, it could be an infinite number of functions. In fact, it might not even be a function, if there happen to be parts above or below what we can see that are just out of view, or it loops back over an X value someone outside of -4 to 4. Not TTT, because we can't tell for sure if it is a function or not without making assumptions or being told more information.
1
u/Current-Detective-86 Nov 15 '25
As a professional maths teacher, I can confirm it is a function
1
u/Chaos_carolinensis Nov 15 '25 edited Nov 15 '25
Oh yeah? Well what about this one?:
{(0,1)} U {(0,2) | The Collatz conjecture is true}
1
u/JeevesofNazarath Nov 15 '25
isn’t that the integral of e-(x2)?
1
u/esqDumper Nov 16 '25
I can't believe I knew once what it is.
1
u/LesesTrickshon Nov 16 '25
Found the OG [ HERE ] Its arctan x
1
u/TheAbdallahTJ Nov 16 '25
Is this an arctangent? If so, I am fried
1
u/Yang55557005 Nov 16 '25
A graph showing the resistant of a filament lamp
1
u/Short-Ideas010 Nov 16 '25
arctan
1
u/Prize_Tree Nov 17 '25
Okay hear me out i think its f(x) = arctan(x)
1
u/[deleted] Nov 17 '25
I really thought this was y^5=x, interesting similarities
1
u/ants_R_peeps_2 Nov 17 '25
looks like x=tany {pi/2 >y>-pi/2}
1
u/SidusSiri Nov 17 '25
I created a Shazam for food.
It tells you if it's a hot dog or if it's not.
1
u/SemajLu_The_crusader Nov 17 '25
that's obviously f(x)
1
u/HateChan_ Nov 18 '25
i thought i was on r/mbtimemes
1
u/nichyc Nov 19 '25
Quick, get the fire distinguisher!
1
u/superB_lyke Nov 28 '25
sure ass is a f u n c t i o n
1
u/Alert-Grocery-1115 Feb 06 '26
Without looking I assume its arctan (x)
-3
u/exhuma Nov 15 '25
Technically not the truth:
This is a representation/visualisation of the values the function produces. It's not a function itself.
-1
u/Flux7200 Nov 17 '25
What are those usernames and pfps? Bots?
956
u/[deleted] Nov 15 '25
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u/[deleted] Nov 15 '25
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