Modeling the equation of a piecewise defined function from its graph (KristaKingMath)

[@Bilbus7]

Omg this was done so beautifully. I love how easy it was to conceptualize. THANK YOU

[@kristakingmath]

f(x)=... means that it's a function, which must have only one output value for every possible input value. y=... is an equation that could have multiple output values for a single input value. :)

[@carstenmeyer7786]

Nice to mention the problem of overlapping domains at the end! ---------------------------- If you know "Heaviside's Step-Function *u(x)",* there is a simpler way to write piece-wise linear functions as sums of step-functions *"u(x)"* and the ramp *"u(x) * x".* First, divide the domain into intervals as shown in the video. The idea is to start at *"x -> -oo".* At each interval boundary, add the step there (if any exists), compensate the old slope, and add the new slope using ramps. ---------------------------- *Example:* Function of this video, but with ℝ as domain. With the algorithm outlined above: *f(x) = [ -0 + (1 - 0) / (1 - 0)] * u(x - 0) * (x - 0) // x1 = 0, E1 = 1* *+ [ -1 + (0 - 1) / (2 - 1)[ * u(x - 1) * (x - 1) // x2 = 1, E2 = -2* *+ [-(-1) + 0 ] * u(x - 2) * (x - 2) // x3 = 2, E3 = 1* *= ∑_{k=1}^3 Ek * u(x - xk) * (x - xk)* *Rem.:* Notice it's very easy to check for correctness -- the added right slope in each bracket gets subtracted as the left slope in the bracket of the next line. The result can directly be written as a sum of ramps (and steps, if there were any). This form is also great for plotting via e.g. gnuplot.

[@syamalchattopadhyay2893]

Excellent video lecture.

[@monicaattia3751]

Sold explanation- very nice! This was so helpful! Keep doing what you do!!

[@OmarioWorld]

Thanks so much! This video really helped! I have a Pre-Calc final tomorrow and I finally understand how to solve piecework functions. Once again thanks and I subscribed and liked just for that! :)

[@kristakingmath]

Awesome! I'm so glad it helped. :) Good luck on your final tomorrow and thanks for subscribing. :D

[@kristakingmath]

Glad it helped! :D

[@ashidilkhan]

Hi will you like to upload mathematical modeling of different physical systems like starting from spring mass system to modeling of aeroplane, motors, cars etc.transfer functions etc

[@MnMn-kx1sk]

How did you know which function to put the equal sign for? I mean why didnt you put the equal sign for the other functions instead for the functions that you put the equal sign for ? Please

[@fairyfairy5388]

Hi Christa I am a fresh graduate of BS physics but I am struggling with calculus I came up with your calculus courses on udemy. I wanted to ask is it worth buying for a BS graduate actually I am preparing for MS admission test

[@kristakingmath]

If you need help with any part of Calculus, then yes! The calculus courses are good for any level. :)

[@GH123XL]

Thank you very much for your help.

[@GH123XL]

Hello. The thing that still confuses me is the difference between y=2x+2 AND f(x) = 2x + 2. Thank you very much for your help. I am following your videos and I like it better than music as my background sound, Lol. Can you believe that.....a calculus lecture as a background sound,hahahahah.

[@feroconi]

hi can u do... time rates and trigonometry? it'll help me a lot. thank you...

[@190hima]

Hi there, how are you? Do you have videos which talk about numerical methods ? thanx alot :)

[@shawnesmailzadeh6279]

Thanks... Really helped out..

[@kristakingmath]

Awesome! :)

[@javieracevesmath]

What program are you using to write with on your screen?

[@kristakingmath]

I explain here :) www.integralcalc.com/how-i-create-my-videos/

[@javieracevesmath]

Thank you.

[@foooof4]

i love your math >> :P

[@franciscoornelas8882]

do you program?

[@kristakingmath]

i have a tiny tiny tiny tiny bit! :) i wish i knew and did more, it's so fun! :D

[@kawsarahmedprince7640]

Thanks :)

[@amadasif1]

lady u r awsome :)

[@ClaudioSoto-YouTube]

Well . f(your_voice) = s + x. I think I understood 😁

[@motazahmed5167]

احمد بيحبيكي

[@OmarioWorld]

*piecewise functions

[@salvador116402]

You are gorgeous

[@SapioSauce]

piecewise OMG LAZY EYE functions