How to Find the Domain and Range of Rational Functions - Number Sense 101

[@TAIIUkA]

He's better than all my past math teachers😅

[@decay8261]

For your example number 5 shouldn't the range also not equal to 3/5??

[@peterveneussvelasco9867]

Sir sa item no. 5, bakit di po na consider yung y=3/5 as excluded value sa range? May parang ganito din pong nangyari sa item no. 4.

[@jay-learnzoe2877]

there is something wrong with your range for question 5 (I skipped the rest of the problems so I didn't check). The range is actually (-∞,0) ∪ (0, 3/5) ∪ (3/5, ∞). Please double-check your work using calculus. One hint is that there is a hole in the graph of the function. Kindly fix this.

[@letslearnvocab3660]

One of the best and most composite video i have ever seen on domain and range.

[@artistic_epiphany]

this video help me a lot in finding the range i have also share this with my classmates. thanks for uploading this now i can pass my mid exams

[@princessleah5896]

New subscriber here, glad I found this vid. Thank you so much for this vid it really helps me a lot..hope there would be more examples of this lesson : )

[@NumberSense101_MervhieCalma]

Sure mam :) thank you so much po 🙂

[@Loading.dot.]

In your example no.6 what if there are no coefficient, like (x+3)(x-2)/(x+2)(x-1)

[@NumberSense101_MervhieCalma]

The coefficient is 1 sir 🙂

[@Loading.dot.]

@@NumberSense101_MervhieCalma Thank you ☺️ sir

[@Loading.dot.]

Sir How do you find the range of f(x)=x^2-5x+4/x-4

[@NumberSense101_MervhieCalma]

F(x) = (x² - 5x +4)/(x -4) The range is from negative infinity up to positive infinity

[@Loading.dot.]

@@NumberSense101_MervhieCalma thank you sir

[@Jay.L_Pro]

Thanks man. This video would very much help me in class!

[@floresneorandeea.6075]

I would like to share this to my classmates

[@jesswealth8213]

Thank you sir Was alot more helpful 😊😊

[@LifasiKhaki]

3 years later it's still useful 😊

[@aby9899]

Thankyou very much sir, this video really helps me a lot

[@jhunmichaelibanez2362]

Sir Face Reveal at 20k subs hahahha

[@NumberSense101_MervhieCalma]

Ahha pag nagkalakas nako ng loob magpakita sa cam :)

[@pol42307]

can you actually find the exact range using the concept of horizontal asymptote alone?

[@lorechadominic4920]

Perfect explanation ever 👌👏thanks 😊

[@hansnaperi8435]

How do you find the domain and range if the rational equation is x²+x-3/x²-25? Same po ba sa example 4?

[@allyssagabriza4320]

Thank you, Sir. I didn't know that you can apply the rules in getting horizontal asymptotes to find the range. 💕

[@NumberSense101_MervhieCalma]

God bless po :)

[@jesusmyking9398]

Here now , new subscriber Thanks sir ,it really helps 😊 ☺ 🙏

[@taiwoawolesi808]

I used to find Range harder... you just made my life easy. Many thanks!

[@owenthies2600]

Thanks its help me

[@abbydevy2415]

Thank you for sharing. I hope you can share as well finding domain for trinomials.

[@vincentvillasante9836]

Can we simplify first the rational expression before we proceed in getting the domain? Take a look at your example 4? Can I say that the domain is the set of all real numbers except except -3.?why do you say that the domain is the set of all real except 3? Since the rational function becomes, f(x) = x-3/x+3.

[@peyt632]

Sir how about f(x)=1/x² . How to find the Domain and range?

[@Adlip_Kun]

Domain: {x/xER, X≠0), Range [0, infinity)

[@portraitmaker5473]

12:50 sir what is in this no.5 what if its like x²-x-27 is there have changes in it if theres 2 negatives?

[@angelaguevarra6336]

Wow thank you sir^.^ Its help me alot!^o^

[@ErmiyasHanchalu-yt5lf]

Excellent

[@neytrilyx7025]

More lessons in math sir hehe thankyou po!!!

[@chrisminebolata7910]

May mali po sa no.4 sa domain except negative 3 lang,,just saying po..sa no.5 din po except negative 3 din and domain.

[@kyleangelobaltazar3368]

sir, paano naman po if n=m? number 5 po hinahanap ko po kasi yung range

[@muhammadrayanmansoor4301]

sir please tell me how to find range if n>m......plz plzzzz

[@michellecatarroja4486]

When I tried to graph the last example using geogebra graphing calculator, the range is different.

[@richloveelizabethferrer8549]

and also how about this find the f-1 ( x) inverse of the function f( x)=x2-144 ----------- x-12?

[@godfreyhaweza3686]

thank you, in 18 minutes all is understood

[@aswellkalawo]

This is how people should teach math simple loud and clear 🎉🎉

[@richloveelizabethferrer8549]

how u get number 1 of in y= 1/x+3 f(x) = x-3 ------- x2-9?

[@kazekya8074]

Damn, you're the best teacher

[@bryangeraldbalucan-sr3zq]

Thank you so much I can now go to sleep

[@-3lnmv7.99]

Thankss

[@ruthdaleon8768]

Thank you so much po sir,ang galing nyo po mag explain mas madaling intindihin,sobrang nakakatulong po sakin videos nyo🥰

[@Mudenda_M]

Your teaching is really great 👏🏾🙌🏾

[@godotavershimadanielharmle5678]

Very clear and understanding

[@kxiju]

#5 is wrong? the only vertical asymptote is x=-3

[@mrlogicodermrlogicoder688]

For e.g. 4 the answer is incorrect as one solution is missing (y cannot be 1/6)

[@Peymk2]

True

[@Peymk2]

True

[@shanelompero9064]

what s the correct answer??

[@mrlogicodermrlogicoder688]

@@shanelompero9064 the correct answer should be all real numbers except y=0 or y=1/6 (i.e. R\{0,1/6}), it's wrong to cancel x-3 directly

[@rovelynhuntahan2079]

How to solve it?

[@sunrisejustkeepitup191]

Sir question po if n>m edi range is no horizontal asymptote po?

[@simondolapo1567]

Thanks so much for this way out...

[@geencaiilemalaguena2474]

Pano po e sulat yung sagot if No Horizontal asymptote sa range

[@danielchibuikem5842]

Thank you very much, you helped me

[@richloveelizabethferrer8549]

how about (f+g)(x)= x + 3and g ( x) =x+6???

[@jedmonicamascardo1257]

Omygod thankyou so much❤️

[@humbertbearthing3092]

Pano kung whole number yung denominator

[@cytus9507]

My head but gotta do all this for a failing grade

[@__ICT__1288]

Hey I have a question, what is n and m?

[@colladomatthews.5343]

Literally the only tutorial i understood

[@KHL4WE]

thank you sir so much

[@cherrylanndones2972]

thank you!😊 it really helped me a lot.

[@estahungebeyehu5354]

Hello

[@notofthisworld5267]

Thank you. Spent 2 hrs now trying to figure this out. You helped 🙂 God bless.

[@MarioSrAlbero]

Pardon me to say this but the range of the numbers 4, 5 and 6 are all wrong. You cannot use the concept of horizontal asymptote in any cases where the highest degree is greater than or equal to two. Graph those functions and you'll find out why.

[@bodhique7626]

ok thanks for the explanation but I am not satisfied. These examples are the easy ones. I am stucked in finding the range of (3x^2-2x+1)/(x-1). Any time that someone makes a video about a topic in mathematics they only show the "ordinary" examples. And then you find yourself having to solve a problem with exactly what the tutorials on the internet don't show. Why you did not include an example like mine? where i) the polynomial in the numerator has no real roots and ii) the function has no horizontal asymptote (it has an oblique one). I hope that someone can help!

[@khairatismail700]

Thnks bro i really like it

[@GB_MathMastery]

hello sire , -thank you for the video it was very informative and fascinating. i have a humble point of vue to add , i think by using the asymptotes method the answer will not always be correct . more precisely if the "m" and "n" are equal, lets suppose you have f(x)=(2x^2-x+4)/(x^2-9) , if we apply the horizontal asymptote method we will say that the range include all the values exept a/b=2 , this can be true but not in real numbers (complex numbers) ,if we draw the graphic representation of this function we will see that we have to exclude another portion where "the delta discriminant of the inverse function is negative" since we are working in the real numbers we cannot suppose that the range include all the real numbers exept the horizontal asymptote.

[@mitangjuice]

thank you!

[@JoeStones-rs2nn]

Life saver

[@aviyanga2216]

Yanga, Maria Avril A. 11-Jacinto

[@johnronaldenverzo6354]

Thank you!!!

[@zenna5062]

How do you figure out the range for something like this? f(x) = 3/x^2-49

[@calistasto.domingo4945]

what if the denominator is simply x²? the domain would be..??

[@abriojhonpouly.8937]

salamat

[@cindychilufya9220]

Wow❤️, finally

[@bwiilomazing7242]

tysm Sir💜

[@jiennacaliloria3691]

salamat po sir

[@princesswellapugoy]

How about naman po sir, if mas mataas ang exponent ng numerator, n>m? paano po isusulat sa final answer?

[@YnaC.]

thank u sm!

[@cancel6122]

sir I love you 😭

[@marielhamida4244]

thank you this really help me,because the struggle is real in rational

[@luismauromaximo3556]

So ibid sabihin po kuya mali yung nasa module yung paraang pagtuturo niya kase iba sagot ko pag sa paraan mo at invalid naman kung sa paraan na tinuro nila...pakireport deped pls

[@myfatherwillhearaboutthis7621]

Tanong lang po, what if lumagpas po ung graph sa horizontal asymptote and decimal po ung max niya pano po makukuha ung exact range po?

[@gray_scale8358]

Sir, question po... Pano po pag walang value yung denominator? Ex po, 2+x/x?

[@muhammadrafidhossain7414]

Awesome

[@lowkeythailook4125]

Sir always bah not equal to zero? nalilito kasi ako sir kung ano gamitin ko kung equal bah or not equal. thanks sir

[@NumberSense101_MervhieCalma]

Ung iba equate nila equal to zero ung iba not equal ginamit. Ok lang naman un ang importante you can determine ung value ng x or y na hindi pwedeng maging undefine ung given na function.

[@NumberSense101_MervhieCalma]

Ako direct ako sa not equal para alam ko agad na ung value na un ay hindi pwedeng maging value ni x or y

[@lowkeythailook4125]

@@NumberSense101_MervhieCalma cge sir thank U may tutorial po bah kau getting domain and range rin po pero ung problem is yong cos sine na

[@spoononacouch2984]

the only video that helped me thank you!

[@LifasiKhaki]

3 years later it's still useful 😊

[@itseasy563]

Best video is history of functions

[@khalcotiangco3270]

how do you find the range of 1/x^2-x

[@yourlolo8969]

sir pano naman po makukuha ang range if n is greater than m?

[@hazelpatani6612]

Para saan po ba yung horizontal asymptome

[@vilmacabuenas9342]

Galing nio po ser, mas madali kaung intindihin kesa sa ibang nagtuturo d2 sa yt🤣😄

[@zzjshpsh]

palagi po bang imu-multiply ang denominator sa y kapag hahanalin ang range? thank you po

[@soloone1410]

Sir sa example 5 bakit po d naconsider sa exception ng range un y value (y = 3/5) ng hole at x = 2? Ganun din po sa example 4 restriction for y = 1/6 kasi may hole at x = 3? Mostly po kasi ng graphing app or range calculator restriction po ang nilalabas for y value ng hole. Thanks po

[@peterveneussvelasco9867]

Yan din pinagtakahan ko...

[@lextersaguibo7876]

Paano po kapag n>m, wala po ba syang range?

[@minatozaki2777]

paano naman po kung mas malaki degree ng numerator kay sa denominator? naghahanap akong videos paano isolve range non pero walang nagbigay ng example na mas malaki numerator sa denominator.

[@tanararp6786]

‘If the degree of numerator is higher than the denominator, the domain of it's inverse is the set of all real numbers’, sabi po sa module namin.😅

[@jasminhipolito8068]

thank youu!!♥️

[@መፍትሄ90]

God bless u

[@tanararp6786]

Sir, pano po if f(x) = 4x lang po yung given. Yung inverse niya po is f^[-1](x) = x/4. Yung Domain po ba of inverse is f^[-1](x) ={x|x E R} at Range is f^[-1](x) = {y|y E R} pa din po?

[@NumberSense101_MervhieCalma]

Domain and range are all real numbers

[@tanararp6786]

@@NumberSense101_MervhieCalma Thanks, sir!

[@lydzchyangelmijares9648]

Thank you so much for this video. Really reliable 😘😘😘

[@princesstrishajalmasco5187]

Sir what if ung denominator po is number Lang siya? For example po is x-7/ 3

[@NumberSense101_MervhieCalma]

All real numbers

[@NumberSense101_MervhieCalma]

Lahat kase ng value pwede. Wala value ng x na magiging undefined

[@princesstrishajalmasco5187]

@@NumberSense101_MervhieCalma thank you sir☺️ such a great help!

[@redstoneclasher2675]

Hindi na yata siya rational function pag ganyan

[@winterland8684]

Sr. Pano po ma equate ang domain if ang given is 3x²-9?

[@NumberSense101_MervhieCalma]

Domain po ng quadratic Function is all real numbers

[@winterland8684]

@@NumberSense101_MervhieCalma same po sa vertical asymptotet? Kase pareha lang naman po sila na equate eh?

[@alikemal688]

Perfect !

[@mdmostafizurrahman7172]

Bad boy.