Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	yesss, exactly!	18,400	31	[]
volunteer	okay, so, f(x) = x^3 - 9 and f(-x) = -x^3 + 9	18,400	32	[]
volunteer	what's true about the relationship of the two?	18,400	33	[]
volunteer	is there an operation you could use to get from one to the other?	18,400	34	[]
student	theyre like the conjugate pairs	18,400	35	[]
student	idk.	18,400	36	[]
volunteer	no, that's a great thought!	18,400	37	[]
volunteer	yeah, the - 9 changed to a + 9	18,400	38	[]
volunteer	but the x^3 switched signs too	18,400	39	[]
volunteer	all of the parts switched signs, here	18,400	40	[]
volunteer	which is equivalent to multiplying by...	18,400	41	[]
student	-1	18,400	42	[]
volunteer	yessss, exactly!!!	18,400	43	[]
volunteer	by multiplying f(x) by -1, you get f(-x), right?	18,400	44	[]
volunteer	so -f(x) = f(-x)	18,400	45	[]
volunteer	and this holds for all odd functions, you should play around with it later!	18,400	46	[]
student	oki	18,400	47	[]
volunteer	does that make sense? it's a pretty tricky concept, I always struggled with it	18,400	48	[]
student	yea i kinda understand	18,400	49	[]
volunteer	alright--we can come back to it at any point	18,400	50	[]
volunteer	just remember for now, -f(x) = f(-x)	18,400	51	[]
volunteer	okay, so lets say we look at the first relationship, where g(a) = -17	18,400	52	[]
volunteer	we want to find what a makes this true, right?	18,400	53	[]
student	uh huh	18,400	54	[]
volunteer	okay, so, let's apply this relationship	18,400	55	[]
volunteer	-g(a) = f(-a) for odd functions	18,400	56	[]
volunteer	so what's -g(a)?	18,400	57	[]
student	17	18,400	58	[]
volunteer	yess, amazing	18,400	59	[]
volunteer	okay, so lets plug that in to our equation	18,400	60	[]
volunteer	17 = f(-a)	18,400	61	[]
volunteer	sorry, g(-a)	18,400	62	[]
volunteer	can you find a place on the chart where g of something equals 17?	18,400	63	[]
student	17,23	18,400	64	[]
volunteer	ooh, close!	18,400	65	[]
volunteer	here, does x = 17 or does g(x) = 17?	18,400	66	[]
student	g(x)	18,400	67	[]
volunteer	looking at the chart, g(x) is at the bottom. is the 17 at the bottom there?	18,400	68	[]
student	yea	18,400	69	[]
volunteer	for which one?	18,400	70	[]
student	12	18,400	71	[]
volunteer	there you go!	18,400	72	[]
volunteer	amazing, okay	18,400	73	[]
volunteer	so if f(-a) = 17, what's -a?	18,400	74	[]
student	wait how am i supposed to know which is g(-a) and -g(x)	18,400	75	[]
student	-g(a)*	18,400	76	[]
volunteer	okay, yeah, sorry!	18,400	77	[]
volunteer	I think I didn't explain that very clearly	18,400	78	[]
volunteer	the thing is, they're equal	18,400	79	[]
volunteer	so either one works	18,400	80	[]
volunteer	we could do it the other way around	18,400	81	[]
volunteer	so like if g(a) was 3 for example, than -g(a) which is -3 would equal g(-3)	18,400	82	[]
volunteer	or other way around, you could plug it into the other side and get the same result	18,400	83	[]
volunteer	I'm sorry, it's confusing to explain it over messages	18,400	84	[]
student	its okayy	18,400	85	[]
student	you can speak if you want 😭	18,400	86	[]
volunteer	I'm in a library :sobs:	18,400	87	[]
student	oooo	18,400	88	[]
volunteer	okay, wait, let's go back to the problems	18,400	89	[]
volunteer	I think (I hope) it'll make a bit more sense afterwards	18,400	90	[]
volunteer	so far we've got g(-a) = -g(a), and -g(a) is 17	18,400	91	[]
volunteer	we know these are equal and there's only one value for a	18,400	92	[]
volunteer	so g(-a) = 17	18,400	93	[]
volunteer	and g(12) = 17	18,400	94	[]
volunteer	as you found out earlier	18,400	95	[]
volunteer	so, what do you think a might be?	18,400	96	[]
student	uh	18,400	97	[]
student	12..	18,400	98	[]
volunteer	close!!!	18,400	99	[]
student	-12….	18,400	100	[]
volunteer	yes!!!!!!!	18,400	101	[]
volunteer	because g(-(-12)) = g(12) = 17	18,400	102	[]
volunteer	so what would a be?	18,400	103	[]
student	uh what	18,400	104	[]
volunteer	you already did it	18,400	105	[]
student	-12?	18,400	106	[]
volunteer	just confirming lol	18,400	107	[]
volunteer	YES	18,400	108	[]
volunteer	amazing job!!	18,400	109	[]
volunteer	essentially, what you need to do for this is solve the equation -g(x) = g(-x)	18,400	110	[]
volunteer	it's just like an algebra problem, except that you have to deal with functions so it's a bit trickier	18,400	111	[]
volunteer	does that sort of make sense?	18,400	112	[]
student	uh kinda	18,400	113	[]
student	lets try to solve for b and maybe ill get it lol	18,400	114	[]
volunteer	yes, let's!	18,400	115	[]
volunteer	okay, so, do you have any ideas on how we can start with this one?	18,400	116	[]
volunteer	(it's okay if not too!)	18,400	117	[]
student	-g(b)=g(-b)?	18,400	118	[]
volunteer	amazing!!!	18,400	119	[]
volunteer	is there anything you can fill in there?	18,400	120	[]
student	-g(b)=11	18,400	121	[]
volunteer	ooh, close!	18,400	122	[]
volunteer	g(b) = 11 for sure, nice find!	18,400	123	[]
volunteer	so what would -g(b) be?	18,400	124	[]
student	ohh	18,400	125	[]
student	-11	18,400	126	[]
volunteer	perfect!	18,400	127	[]
volunteer	okay, so now we have -11 = g(-a)	18,400	128	[]
volunteer	any ideas of where to go from here?	18,400	129	[]
volunteer	do you see any g(x) that equals -11?	18,400	130	[]

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