Getting equation from this unknown graph[tried everything) | Mathematics | Page 1

brazen glen Jan 3, 2024, 2:14 PM

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So been dealing with quite a challenging problem of trying to get the equation for this function or even defining it because it is so crappingly drawn it defies form(the example graph is more curvy upwards at the end while mine is a consistent curve towards the end towards positive infinity.I guess browsing free textbooks pdfs on the internet, you get what you pay for. From my work the equation seems logarithmic because the equation hits all the points(starts at negative 5,crosses y axis at 2 and resembles the curve shown in example graph, it just looks different. Accompanied is also my algebra work on this problem. Thank you for the help!

random crownBOT Jan 3, 2024, 2:14 PM

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brazen glen So been dealing with quite a challenging problem of trying to get the equation f...

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brazen glen Jan 3, 2024, 2:15 PM

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though im starting to think it's exponential but am not sure i did calculations and equation just didnt match,will do these again

sonic hollow Jan 3, 2024, 2:26 PM

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brazen glen

this is more cubic/odd degree polynomial than anything

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like the blue one has a horizontal tangent at 0, logs dont have critical values where their derivative is 0

brazen glen Jan 3, 2024, 2:29 PM

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ah it smelled like cubic little to me.hmm will have to do calculations over again.though to me it seems like a polynomial more

sonic hollow Jan 3, 2024, 2:29 PM

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... cubics are polynomials

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they're polynomials with degree 3.

brazen glen Jan 3, 2024, 2:29 PM

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ah my bad

sonic hollow Jan 3, 2024, 2:30 PM

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But yeah, that picture is clearly not a log

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the arrows imply the domain is the entire real line

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logs have vertical asymptotes

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logs dont plataeu anywhere

brazen glen Jan 3, 2024, 2:32 PM

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though idk how would i form an equation for this considering it only has one x value of -5

sonic hollow Jan 3, 2024, 2:33 PM

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well you know it's of the form $p(x)=a(x+5)(x^2+bx+c)$, so use the other aspects to find $a,b,c$.

sharp urchinBOT Jan 3, 2024, 2:33 PM

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Omegabet_

brazen glen Jan 3, 2024, 2:33 PM

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okay

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thanks

brazen glen Jan 3, 2024, 4:01 PM

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can anyone explain how to do the calculations ahead,i tried synthethic divisions but didnt get many results :/

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i think long division might be neccesary here?

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with like the whole polynomial instead of the factored form?

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nermind im a moron,i think i know my problem now

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i foiled the placeholder b which i likely shouldnt have

brazen glen Jan 3, 2024, 5:18 PM

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Getting equation from this unknown graph[tried everything)

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so now I tried the cubic form as suggested and it didnt give me any graph,what i managed to come up only is an equation that doesnt give me any graph.
here is my work

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so its maybe a cubic,not a quadratic,not an exponential,not a logarithmic. idk anymore tbh

opaque wraith Jan 3, 2024, 5:26 PM

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brazen glen

is this drawn according to scale

brazen glen Jan 3, 2024, 5:27 PM

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idk seems quite poorly drawn if you ask me

opaque wraith Jan 3, 2024, 5:27 PM

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brazen glen

you can interpolate it from 4 points that are visible

sonic hollow Jan 3, 2024, 5:27 PM

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well like I said at the start, from guessing it's a cubic and knowing x=-5 is a root, you know $p(x)=a(x+5)(x^2+bx+c)$, you also know $p(0)=2$ and $p'(0)=0$ (or at the very least, those are immediate, approximate features)

sharp urchinBOT Jan 3, 2024, 5:27 PM

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Omegabet_

opaque wraith Jan 3, 2024, 5:27 PM

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P(-5)=0
P(0)=2
P(3)=4
P(4)=5

sonic hollow Jan 3, 2024, 5:28 PM

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2, not -2

opaque wraith Jan 3, 2024, 5:28 PM

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right

brazen glen Jan 3, 2024, 5:28 PM

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i dont get p(3) and p(4)

opaque wraith Jan 3, 2024, 5:29 PM

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you'll see it if you squint hard enough

sonic hollow Jan 3, 2024, 5:29 PM

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approximately, p(4)=3 amd p(5)=4

opaque wraith Jan 3, 2024, 5:29 PM

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5->4?

sonic hollow Jan 3, 2024, 5:29 PM

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blue graph is the cubic

opaque wraith Jan 3, 2024, 5:30 PM

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i was talking about the purple

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it's also a cubic

brazen glen Jan 3, 2024, 5:30 PM

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the purple doesnt matter i need the blue one

sonic hollow Jan 3, 2024, 5:30 PM

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inverse of a cubic isnt a cubic though

opaque wraith Jan 3, 2024, 5:31 PM

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i mean is it really the inverse

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or is it reflected along y=x

sonic hollow Jan 3, 2024, 5:31 PM

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it's symmetric about y=x

opaque wraith Jan 3, 2024, 5:31 PM

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ye

sonic hollow Jan 3, 2024, 5:31 PM

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so yes, inverse

opaque wraith Jan 3, 2024, 5:31 PM

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dog

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yeah sure just find the cubic and solve that shit

sonic hollow Jan 3, 2024, 5:32 PM

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brazen glen the purple doesnt matter i need the blue one

but anyway yeah, you can just eyeball the couple points on the blue curve and determine the coefficients of a cubic that passes through them

opaque wraith Jan 3, 2024, 5:32 PM

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honestly a dick problem to be blunt

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points appearing to be on convenient integer points

brazen glen Jan 3, 2024, 5:33 PM

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which coeficients are relevant for blue graph only?

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im guessing
P(-5)=0
P(0)=2
P(5)=6

sonic hollow Jan 3, 2024, 5:34 PM

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those arent coefficients, those are the conditions your cubic must satisfy

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you can guess $p(x)=ax^3+bx^2+cx+d$ then plug in all those condititions to get a system of (linear) equations in the unknowns $a,b,c,d$

sharp urchinBOT Jan 3, 2024, 5:35 PM

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Omegabet_

opaque wraith Jan 3, 2024, 5:35 PM

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catThink or you could interpolate

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pick your poison

brazen glen Jan 3, 2024, 5:36 PM

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i pick system of equation,dont know how to interpolate yet

sonic hollow Jan 3, 2024, 5:37 PM

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yeah, the system is just a 'standard' computation, or you throw it to a computer

opaque wraith Jan 3, 2024, 5:38 PM

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dog

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,w interpolate

sharp urchinBOT Jan 3, 2024, 5:39 PM

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opaque wraith Jan 3, 2024, 5:39 PM

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@sonic hollow yk how it work?

sonic hollow Jan 3, 2024, 5:40 PM

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I assume you mean Lagrange interpolation, but it just obeys a formula

brazen glen Jan 3, 2024, 5:50 PM

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so just to confirm so i dont mess up,the conditions for blue graph are:
P(-5)=0
P(0)=2
P(5)=6

? or am i missing some?

sonic hollow Jan 3, 2024, 5:51 PM

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brazen glen so just to confirm so i dont mess up,the conditions for blue graph are: P(-5)=0 ...

from having eyes, you can see p(-5)=0, p(0)=2, p(4)=3, and p(5)=4

brazen glen Jan 3, 2024, 5:52 PM

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ah ok my bad

opaque wraith Jan 3, 2024, 6:00 PM

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sonic hollow I assume you mean Lagrange interpolation, but it just obeys a formula

the command in wolf ram i meant

sonic hollow Jan 3, 2024, 6:00 PM

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nope

steep leaf Jan 3, 2024, 6:35 PM

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if p(4) = 3, then p'(0) =/= 0
i would just go with p(-5) = 0, p(0) = 2, p(5) = 4, and its an odd function except for being moved up

brazen glen Jan 3, 2024, 7:53 PM

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so i made the calculations and came up with these results,inserted them into functions and still dont get the same graph at all.this is starting to look like a sadistic troll exercise

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this is the og function i am looking for the blue one..

grand creek Jan 3, 2024, 7:57 PM

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brazen glen this is the og function i am looking for the blue one..

Well, seems to be of the form y = ax^3 + 2. You can find a by noticing it has a zero at x = -5.

brazen glen Jan 3, 2024, 7:58 PM

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.5

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-5

grand creek Jan 3, 2024, 7:59 PM

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Right, sorry.

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Corrected.

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So, have you found it?

brazen glen Jan 3, 2024, 8:01 PM

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doing calcs

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will be done soon

grand creek Jan 3, 2024, 8:02 PM

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Alright.

brazen glen Jan 3, 2024, 8:04 PM

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found it,its 2/125 x^3 +2

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i mean the whole function

muted patioBOT Jan 3, 2024, 8:05 PM

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grand creek Jan 3, 2024, 8:05 PM

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brazen glen found it,its 2/125 x^3 +2

Yeah, very good!

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And now you can find the equation of the inverse red function, too, if you need that.

brazen glen Jan 3, 2024, 8:06 PM

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yeah i will tomorow im tired spend whole day on this example

#Getting equation from this unknown graph[tried everything)