[Music] Aloha my so then the eternal mind I hope I might be gay now continue I love and saying yeah so our lessened it is to find domain and range in even the different relations said to some our topic now major nagulu a number I'll add another part equation and keep in so raycoleman attire so what is the domain is the set of first coordinates range is the set of second chord you need so you first coordinate that is the x-values non-sag repeat again and range the second set of values or the Y values swish and Yong Seon gag a meeting at then to find the domain and range so be began go by now different examples and then I had not be nothing in domain and range so here maritime the level many people a I was sending that but you can dine Kappa given an equation so presented below are some restriction to consider in finding the domain and range of some function that involved the following first radicals with even indices so radicals must be non-negative so that part equal and opposite you know are greater than zero sewed up in disappeared imaging negative numbers bowel urine follow-up fractions denominator must not be equal to see so I'll undermine not and any number divided by zero the answer is undefined so that but in Demon's equals zero um denominator my specially cap again I rationale No so start taya I'll give you a set of examples to find the domain and range given the following relation first given the ordered pair so the relation F is equal to the set of one two two two three five and four five so I know I am domain and range not end so Saba canina the domains the first set okay for the first coordinate and range is the second coordinate so under be my first call coordinated on so what two three and four so therefore Union domain had been so Miss mcgoun declares Kappa halimbawa addition of ascending order so the origin is nothing insecure in ascending order but at important tito new bracket network so he picks a pink ACN Sinha sobbing and that is the set of the X values or the set of the first coordinate next is the rain so pinion ties up Paula WA so maritime two two five five so II thought Delaware internet and so Cooney like nothing said no so five so therefore you arrange not in journeys two and five so Madeleine Kunin in domain and range Kappa given an ordered pair another example so we have 1 negative 1 2 and negative 3 0 5 negative 1 and 3 4 negative 5 negative 1 & 5 4 and negative 4 so no pain domain endings so so deep in maritime 1 2 0 negative 1 for negative 1 4 so Indiana higher snow so miss madenda arranged not in our using the number line so good night moon and not in Amman negative numbers so the domain is negative 1 0 1 2 & 4 so next is a negative 1 but it's a good you know organized a pad so my tee time in forecasting it should know it then the value of the inch we have negative 1 negative 3 5 3 negative 5 pipe and negative work and and then so similarly millinery some are negative numbers so we have negative 5 negative 4 negative 3 negative 1 3 & 5 again kappa even in ordered pairs so can an onion gaga win you so mad about making organized since I could not in another couple given new mapping diagram it on Appa utterly lengthy nano keep Ankita so you if you you know you're in what is the x value so I am nothing about your x value that is the domain and then this one your output or the Y values that is the range so teeny not an uneven x-value snap end we have a b c and b then you arrange net and we have X Y and C so they end up upper keep in your mapping diagram so Allen Bauer dope a young a nap in detour so it's a linear I represent get on set on menu given the table of values okay given the table um participant in the nothing class you arrangement yeah papa back on ascending or Dana say Dominica along and Lina Silla Kayla and buggy oh bugger organize now so what is the domain in the set on the first table of values negative seven negative four to eight ten and nineteen so it to yon and then for the value of range we have twelve nine negative eleven seventeen six and negative five so Diana Sanada cocaina so nine Mona not a no in ascending order we represent your answer in ascending order so start like a negative 11 negative 5 6 9 12 and 17 so so far 11 table of values the domain is negative 19 negative 6 to 1 to 15 and 18 so again Deaton you learned imitating man you arranged the Amanda tournament eating and so I need a pat on my own again of course negative 20 negative 3 4 8 9 and 16 so Madeleine Kunin you don't mean in range kappa canyon and keep n cap an ordered pair mapping diagram and the table of values so another example is hissing the graph so panel not in malpua you domain in range from the graph so my key tenets in dito you grab not in finite now okay so negate and shut it off ito my endpoint you graph and then the endpoint yeah okay shaded topics Ibiza being a saner shade it's a graph Ibiza PN Casali on Casali appointment Soyoung eating at all and the new tree is a part of the solution you negative 10 and negative 2 is a part of solution so that and then attend couple never shaded in circles same point on graph it's a being that is a part of a solution so again by the not emo Hawaiian domain and range and Gannon London so you X values no your X values in heating and nothing's that don't mean so uh nobody toy detour ie to me in Italian grab not end so tipping then you own an illness are kupdegra so similar ties champagne from left to right so any is negative 10 D to Munna repeating and paramita1 napping and dawning Jam sown again chess a negative 10 and then up to negative 2 so therefore he picks a being known under me nothing i mullah ok negative 10 up to negative 2 so a big CBN topic Milligan attend cop tiny topic Milligan Athena's interval notation they need to share Kappa included know ABC we negotiated share and gaga meeting a tourniquet bracket and bracket the new velena learn and become so from negative 10 to negative 2 if we say BN our solution London Gretna and is from negative 10 to negative 2 again only think o kapa haka shaded in circular young endpoint no grab epics opinion ksama it's a solution you pandaman you arrange a by the way nila get to class Casa means an AHA dependents are teaching your animals in a good new by interval notation and Senecas interval notation environments and a set notation capacity notation eaten a man X such that your X is greater than or equal to negative 10 but less than or equal to negative 2 magnitude in Iowa of course I mean we're not in the domain is shown X so on X belong down so my handgun and Lang greater than or equals K negative 10 but less than or equal to negative 2 so he too long it apart long network under menu so you arrange them and determine by fitting in it also critical in at also Y values so I don't eat in an ar-10 will send a young to learn and graph so in doodling graffito sunny and three Ito 18 say big Sabean from 3 to 18 you arrange not n so 3 to 18 so therefore your Y is greater than or equal to 3 but less than or equal to 18 so getting input 2 mu 1 and dominant rings I grabbed pan in a man kappa Jenny Tong he pen and me song he's an endpoint Naha open insert hell no Anisha say that and Sabich oakarina have exceeded kasama solution but unshaded hindi Kazama soap Anna Nardini represent you know minion canina this is a una example de Graaff natal they represent that in Japan Kazama bracket dito enough iron symbol gamete in a pen so we use this open parenthesis no potato Kappa Hindi Kazama and Capaldi Shabazz Amano and then this one bracket there Kazama knavish a dead now so panel it not including in domain and range Sheraton dito so sunburned again Tim grab okay negative 1 bar by negative 2 k- fiber so d2 Chateau moppet a zero and then hand ends on a positive 4 so a big serbian mula i to hunger no innocence this is very not okay similar greater intentions is 0-2 for you except en so you range you all your eggs should be greater than 0 but less than or equal sephora bucket eternal belong equal casa andina Montes arm sec you know adenosine RB cornica open your circle now the addition of a shaded so you arranged the Manhattan again the entire detours a practical value vertical line at all alright the Y values sunburn against anti TT n couple kisses her range class gamut um graph pagani to tie up up here s in an idiom about all values of a bad okay so d2 time at start since um last not grab no to my part a negative 4 so start yank a negative 4 up to positive plants ok none among a array your Y values is greater than or equal to negative 4 but less than 1 so again so hope I ranging in a hand up not n so d totemic see similar but pocket I of Kapaa comedian grappa so NATO my perfume graph not answer negative 4 and then up to positive 1 since neva shaded though so therefore you make a deferred customers arrange not end so y is greater than or equal to negative 4 but less than 1 so ganyan kappa given and grab another parliament kappa gangin young crab nothing on america tonight and mention I know aerobics have been infinite know infinite way longhand gaan sao paulo not emo hawaiian domain and range yen so from negative infinity to positive infinity so he picks up en your ex is a set of all real numbers so lahat kasama kappa ganito class so long endpoint um grab nothing so he picks a being all real numbers since a good meal Kappa Gamma interval notation eaten got a meeting in simple there are parentheses from negative infinity to positive infinity couple set notation X such that X is a set of all elements of all real numbers next tenant in kappa range say infinite Nashua - an endpoint so we're gonna need him at the inside you know your why is a set of an element of all real numbers Appa Gannett on given a graph now along in points so you need to make me select near all real numbers when Appa get it or you need some direction on grab me on this one infinite Shah and Ito may end point so annoying domain and range not engine again but cotton and domain anything an attendee toe-cap atom in a man like start I'll of course from left to right okay so from left to right tire my kid I know dito young grab not in his infinite in a big Sabean were okay too late to the yen therefore Indomie not and is from May in Feeny P na Nana na insecure to positive 3 Buffett parentheses and gamut nothing Cassie class na Openshaw initial shaded if it's a BN y or X is less than 3 in the body of your domain is X less than 3 so melody toe K 3 papa except 3 of a X is less than 3 so similar journey I got a punt on negative infinity under the manually in Staten cappuccino who under my new range from both all our prom down to s 1 ok Milazzo baba back yet again and then Melissa Baba parkette ad from negative infinity didn't talk to positive 16 so here Y is less than 16 so again like biggy I was singing and up at the class in and growl Camaro on Kundalini toy operating in am Impala can sit in a pan hakuna mean domain and range Kappa given an equation that and the analogue e-class kappa dom perignon x and y no polynomial and a secondary set of all real numbers except sorry in scuppered my restriction again it as a number 1 - x - y equals 5 to find the domain sold for y ok kappa kappa Linehan up nothing in domain it's a salt not a new equation and in terms of Y so of course but engineering equation y ou D but not is it - extra Billa negative y equals negative 2x plus 5 since negative you know why not then I'm gonna go I'm not ending it if I'd not is a negative 1 both side Oh pea EMU multiply negative 1 but I knew you why MIDI game positive so you negative 2x making positive 2x and then you find me negative 5 then anong ginagawa not then we divide nothing a negative 1 or multiply by negative 1 so not go any naught and this is the body of y 2x minus 5 and since Y is a polynomial again a polynomial and why not and therefore the domain is a set of all real numbers for learning a bicycle chain set of all real numbers a dinner Kappa why no polynomials or new class simple enormous study but that will be binomials okay so this is your domain the set of all real numbers to find the range solve for X so copper green tourmaline and AB not an issue so Nadia equation for x so 2x is equal to 5 plus y so see negative y nominally but not in cerebellar since Marin time constant my constant that asama young X and Ungaro in a 10 if they divide both sides by 2 so forgive me white both side by 2 2 X divided 2 that will be x equals so muddying y over 2 or 1/2 y plus 5 over 2 so again this is polynomial well our restriction dito so third for young rain/snow is what what will be the value of your range that's also that's also so you be shall be a new range net then set of all real numbers then k c---one our restriction and your X is a polynomial so this is X now I need a Nepali pen okay so your X is a polynomial without restrictions so therefore you range not and its only numbers so I'll give you another example y is equal to x squared minus 9 so gonna know let to find the domain solve for y so since it's already express in terms of y know so my value negative Y naught and this is also a polynomial so therefore the domain is a set of all real numbers so all the time problema didn't happen Kalyan and don't you you know what not inside on Young ik support we on to find the rain-soaked Forex it okay Lana 10 so y is equal to x squared minus 9 this is the original equation sold for X so lipid not is CX squared so negative x squared is equal to negative Y minus 9 so back at any negative Y so mullet eat accessibility but not in be torn every negative Y so again their negative u x squared nothing go in at in pass it here by multiplying both sides by negative one so buggying x squared is equal to y plus 9 so I know money on each end by using square root method but Makua not a new X square method longer a meeting that and your X is equal to positive and negative square root of y plus 9 merit are you married on Vinny taken in and a couple radical zoom given are you value non ex or my no DAPA Yunus elope I must be 0 or greater than 0 so DARPA initial multi- so far nothing una Y on your y plus 9 equate you by greater than or equal to 0 so therefore y must be greater than or equal to negative 9 so nobody in in jail and human being range huge and so copying a long talk okay so why is a said oh no Y such that Y is greater than or equal to negative nine so you know my given value no range no again bucket making any times I could not in the same a restriction Tyson article stop bug radicals in value non ex newer why Kaelin equal to zero or greater than zero so you know an attempt armoire nothing imaginary inched in equate 9a y plus nine greater than or equal to zero so therefore if you buy an orange netting I'll give you another example x squared plus y minus 4 equals zero so repeating energy equation D position R is to find the domain solve for y so again using this equation so that in cy x squared plus y so c- poorly but not in Serafina and then CX squared Lee patty not is fabulous so muggy in unity and Y is equal to positive four minus x squared so Ito I polynomial now so therefore you're dominating journey is a set of real numbers bucket any value of x Marin Kallang one value of y know so therefore that is a set of all real numbers whatever restriction Yin how about the value of being sold for X no man x squared plus y is equal to 4 so lipid natin see why Cassell Nenana Platinum X in volume and X so x squared is equal to 4 minus y then using the square root method X is equal to positive and negative square root of 4 minus y K diet vanina's example number E so my restriction tired appetito I greater than or equal to zero so in a bustling adding n 4 minus y greater than or equal to zero so therefore your y must be less than or equal to 4 sorry about it looking like BOGO you inequality symbol yeah a greater than demand Ito but it on again less than Cassie class you why not in detour negative okay so para mugging and again positive we need to change the inequality symbol or the top engineering a multiply both side by negative 1 so much change you under nothing but you change the inequality symbol in a 10 so therefore you range is y less than or equal to 4 so getting done so top and I need a gear my restriction a beanie big echo saying yo kappa radicals he picks happy ending even now arm bearing indices Kalyan greater than 0 or equal 0 top at Lonnie talk so cannon on yanagawa here in Alabama Lanyon you know my game piling on arrange new necks so this is the last example it will be like a saying you 3y plus XY is equal to 2x plus 1 to find the domain solve for y so again I'm gagawin a 10 it's a short not in CY in Delhi 1 my YP toe and on Gargery not in so you could group not I know it for factory not into là-bas not in C Y so Y so 3y divide Y so that is 3 copy the sign plus XY divided by so Mediteranean X so Marinette ID 2 y times 3 plus X is equal to 2x plus one bucket millibar CY kasi class Y and Kalon adding is para maha nothing in doing since Merrin Kazama see why do we need to divide both side by 3 plus X so I can invite not in it though so 3 plus X or Mediterranean Gen Y and is equal to 2x plus 1 over 3 plus X rational and by you know why not been so big a fraction share my restriction subtraction right so Ananse restrictions abruption Kayla and Hindi Mugsy gyro and denominator no a sec opponent equals at zero in denominator in a 10 let's say young X mati tiny negative 3y except en and define your value no why hey I'm Godwin at them quick moon and a teensy denominator so 3 plus X should be not equal to 0 so no gagawin at him so X is not equal to negative 3 so the pattern not into 3 sabila so therefore you arrange i indomie not in detour your X is a set of all real numbers except negative 3 so muliple not a negative 3 ksama lahat embodiment x malignantly negative 3 so again sorry because saying your topic rational fraction ulama bus stop at Hindi atomic in Syria on denominator so he came in anger doing a 10 to find the result for X so 3 y plus XY is equal to 2x plus 1 so X and in a Hannah ready potato on the lower pecs are Maya in there siddhappa you may press the my ex siddhappa atomic Kazama so I know gallery not a leap at night in situ X acapella C 3 wife anybody not in sevilla so beginning and the end XY minus 2x is equal to 1 minus 3y sabaha Taylor and lipid C 2 x2 say he tuned delawanna type but I asked my ex my common viable Scylla soap Aramis hopes ax divided not in it boss say X so X Y divide X comma T there and along y 2x divide X ma TTI sir - since makers are my X naught then we divide not in both side by y -2 so your X now is 1 X is equal to 1 - 3 y over y -2 again my restriction of entire del traction and sir good rational and say goodnight so that part and why not what I'm denominator not in a Hindi department equal to 0 so I'm gathering down y -2 should be not equal to 0 so me array Y is not equal to 2y big cbn wise a set of all real numbers except positive 2 so lahat kasama some Y values malli balance a positive 2 so now I know no I knew how to find the domain and range given the different given they for example ordered pair mapping diagram and drops of course and then the equation so so much for that case I say by the man he discuss them and how to find the domain and range so indigo is a sardine as a discussion at all susannah mean and to tune and Colicchio so thank you so much senility new a benign or pan Iranian XP gentleman and don't forget to Like subscribe and hit the button well what am I notified kazar me channel so don't forget to subscribe while my channel Marama kamini upload soon into the data Selina Ito general mathematics monitor for that thank you