A-Level Maths: B8-03 Functions: Examples of Finding the Domain and Range

[@louiepeters4759]

why are teachers on the internet so much better than ones in schools?

[@PLScience]

They teach without any restrictions.

[@alexaarenstrup2883]

Because the viewers select the teachers by choosing who to watch whereas teachers in schools are selected by people who aren’t students

[@abdullahahmed3843]

@@alexaarenstrup2883 good economic theory

[@davidcunningham6177]

Because you can pause and rewind when you want...and they can edit and repeat without you knowing. In reality if teachers make mistakes you see them, and if you don't understand you probably don't ask the teacher to repeat it because you don't want to seem stupid

[@samayahone3497]

Because you can pause and rewind, and work at your own pace! Plus they can edit out the bits where they make mistakes and jumble their words, and they can write scripts and such to make it more coherent :)

[@mohamedasef5376]

thanks to TLMATHS, this is so easy and comfortable to understand with many separate details, pls continue to upload more content of a level

[@aaryanramani1699]

You single-handedly saved my AS Maths grade. Amazing job Sir!!!

[@aaryanramani1699]

Here for A Level Mocks as well...

[@aisyahfarah8100]

you are a lifesaver, i have my igcse addmaths tmr and i finally understand functions thanks to your videos

[@ashh4550]

thank you so much that made so much sense and was so much better than what my maths teacher taught me irl, hes a really good teacher but on range and domain i got very confused and now i understand it thank you so much!

[@brokke8388]

thank you so much! you make everything seem really easy

[@tapiwanashegumbo8937]

I just want to say thank you so much may you be blessed with incompatible blessings

[@olakitanemmanuel7531]

Nice knowing you sir. Could you pls make a video on how to find the domain and range of a modulus function. Thank you sir.

[@TLMaths]

What problem are you having specifically with modulus functions?

[@ilyazueen]

litterally my life saver 😭♥️

[@tallula5164]

am I being too pedantic that for y=e^x as there is always an asymptote the x-axis, this means there will always be a value between the axis and the function which shouldn't be included in the range? or is it because this value will be so insignificant and small we do not need to include it? many thanks

[@enochp.3547]

For the 5th curve, f(x) = e to the power x, how did you determine where the graph crosses the y axis

[@TLMaths]

You can determine where a curve crosses the y-axis by substituting x=0. So e^0 = 1

[@najwarae8640]

What does the e mean

[@TLMaths]

From F1-07 onwards: sites.google.com/view/tlmaths/home/a-level-maths/full-a-level/f-exponentials-logarithms/f1-exponentials?authuser=0

[@puddleduck1405]

@@najwarae8640 its a constant, like pi. its called Euler's number and is 2.718...

[@taetae9375]

You are a life saver!!!

[@Masowe.]

8:08 can i say f(x)>/=1 because the graph always cross at 1?

[@TLMaths]

Only if the domain was x>=0

[@Masowe.]

@@TLMaths thanks sir

[@mohsinnaqvi5516]

hey b0sS. you are great. any advise on as exams?

[@TLMaths]

Once you're happy with understanding, you need to work through all the past papers you can (around this time you need to be putting yourself under timed conditions and completing them in a single sitting - do not look at the mark scheme at any time until you mark it at the end).

[@mohsinnaqvi5516]

thank you very much.

[@ravjayakodi2746]

why is this topic harder than integration ? 😭😭😭😭

[@Awai_quotes]

Hey sir i wanna ask at 3:55 instead of f(x)>0 can we write that f(x)belongs to natural numbers?

[@TLMaths]

No, as the natural numbers don't include 2.5, 3.7, pi, etc.

[@NikV01]

Thanks Sir. Video was very helpful

[@steenmin]

Great video dude 🔥🔥🔥

[@KA-xw3th]

Thanks for the video. I really appreciate 🙏 💛 😌 ❤ 💓 💕 🙏

[@KA-xw3th]

Pls is there a way to determine the range and domain of all these functions without necessarily sketching?

[@TLMaths]

Not really - you need an appreciation of what the graph looks like to determine the domain and range.

[@sahilpahuja7703]

Hey sir just had a doubt, Do they give these graphs already with the question or you have to figure them out and if yes then could you please let me know

[@TLMaths]

Range and domain questions for more complicated graphs will likely be there for you. But for all of the examples in this video, you should definitely know how to sketch each of these graphs.

[@sahilpahuja7703]

@@TLMaths thank you so much, very glad to get such an early reply from you. My best wishes for this channel. Love from India

[@kevinjanuario4608]

great video but for the 6th example f(x)=lnx shouldn't the range be f(x) belongs to any real numbers but can't = 0 as it never touches the y axis

[@TLMaths]

f(x) can equal zero as it crosses the x-axis, I think this is what you mean.

[@kevinjanuario4608]

@@TLMaths doesn’t the range depend on the y axis not the x axis?

[@TLMaths]

The range is concerned with the possible y values that can be reached by the function. ln(x) = 0 when x = 1, so f(x) = 0 is not a problem for the function. Hence f(x) belongs to the real numbers and there are no other restrictions on the range.

[@Anne-hu4ve]

This is very helpful

[@lailafida7554]

Hello sir.can u plz find domain and range of modulous functions???

[@TLMaths]

Here you are: kzbin.info/www/bejne/kHXKkqKFa66ihtk

[@clyven8727]

Thanks a lot, how to find domain and range using use of graph?

[@TLMaths]

The domain is all the values of x that the graph exists for. Keep an eye out for vertical asymptotes! The range is all the values of y that the graph exists for.

[@hamzaahmed5436]

@@TLMaths hello sir I was wondering how to do the same with parametric equations after we turn them to Cartesian equation. Cuz it gets hard of how to draw the graph then. Thanks a lot

[@TLMaths]

@@hamzaahmed5436 Again, you'll be looking for common situations like dividing by zero, and square rooting negative numbers, etc in order to determine the domain. The range of values can be a lot harder. I can't remember seeing any questions on A-Level Maths where you're asked to do this though.

[@hamzaahmed5436]

@@TLMaths it was on my exam question on Pearson active learn (I do Ed excel maths) and it asked me for it after getting the Cartesian equation. Because of this I really struggled.

[@TLMaths]

@@hamzaahmed5436 Can you remember what the parametric equations were? Just so I can guage difficulty

[@datuklofi]

Is there a video of you teaching how to sketch the graphs?

[@TLMaths]

You can find a host of sketching curves videos here: sites.google.com/view/tlmaths/home/a-level-maths/full-a-level/b-algebra-functions/b7-graphs-proportion

[@youssef5263]

Wait, I don’t understand how u drew the e or inx graph

[@TLMaths]

e^x kzbin.info/www/bejne/hpSvk2yhd5x0gtk ln(x) kzbin.info/www/bejne/d4uxgKOQj7-Ylbc

[@youssef5263]

@@TLMaths Thanks for the help

[@mangelo_1855]

for the range of Sinx, could you say /f(x)/ < 1?

[@TLMaths]

The range of sin(x) is -1

[@soreszzio3792]

Life saver 👍👍

[@leahlester2620]

do we need to know how to find the domain and range of 2x+9/2x-1 for example

[@TLMaths]

I would say yes to the domain (as you just need to be able to identify when the denominator is zero to answer this). As for the range, I'll check with awarding bodies - I'll let you know what I find

[@leahlester2620]

@@TLMaths Thank you for your prompt reply! Thank you so much for your videos they are helping me ALOT!!

[@leahlester2620]

@@TLMaths Just wondering if you got an answer from Edexcel. thanks!

[@TLMaths]

No, I don't think I ever received a reply. I would probably say that it is worth you knowing how to find the range of such a function (by recognising that there is a horizontal asymptote at y=1). www.desmos.com/calculator/zbwdalumyg

[@leahlester2620]

@@TLMaths thank you!

[@oskarwitha_k8258]

for number 6 you said that y can reach anything below the x axis but it will always be positive right, it isnt possible for it to turn negative or is it?

[@TLMaths]

The range of y= ln(x) is any real value of y www.desmos.com/calculator/yggdbpn1dh

[@oskarwitha_k8258]

TLMaths thank you!!

[@celeb3921]

No 3 is incorrect to me cause I don't know why the line doesn't pass through 0

[@TLMaths]

When x = 0, y = 0^3 + 1 = 1, so it doesn't pass through the origin

[@sajadalkarim7205]

In the real exam, should I remember all of these graphs?

[@TLMaths]

I would expect you to be able to sketch any of those graphs, yes.

[@Doodo981]

For graph number 4, why isn’t it shape as a quartic

[@TLMaths]

It IS the shape of a quartic, but you've only got one in mind. Here's some on Desmos you can have a look at: www.desmos.com/calculator/dvxrax2gve

[@betul-ev2fu]

thanks

[@Braekuh]

My man if we knew how to make the sketch everytime then obviously it's easy

[@TLMaths]

That's why you gotta practice

[@muhammadshaheer4766]

Does this playlist cover the Cambridge As level syllabus?

[@TLMaths]

The playlist isn't designed for the Cambridge specification. There will be quite a lot of overlap however - you should check the spec document to see what is/isn't covered.

[@apatchy0664]

Is this for AS maths

[@TLMaths]

No, all of the videos for AS have titles that are in [square brackets]. You can navigate them all more easily here: sites.google.com/site/tlmaths314/home/a-level-maths-2017/as-only

[@talh.a]

TLMaths There is no topic for functions in your link. Pls guide. Has the syllabus changed? I have test tomorrow so a fast reply would be grea

[@TLMaths]

Functions (incl range and domain, inverse functions, modulus functions, etc) is not AS-Level

[@talh.a]

TLMaths I have been taught the whole chapter at school. It is also included in the P1 syllabus given on Cambridge website

[@TLMaths]

I can only speak for England's A-Level exam boards

[@itsfuckintreyyyway7881]

cheers lad

[@cannerz4073]

🐐