1 HOUR ASMR - study with me✍️ tapping on tingly triggers 💞

Added: 2026-05-12

[00:00:06]Hi.

[00:00:08]Um Sorry.

[00:00:11]Okay.

[00:00:14]Um today I'm going to do some tapping and also do some work because I've got a lot on here.

[00:00:30]Hi.

[00:00:33]Um I'm going to do some maths today because well I need to make a video and I need to do maths. Why not kill two birds with one stone?

[00:00:48]So So here we are >> [snorts] >> pretty much.

[00:00:59]Okay.

[00:01:11]So I have a book of work from law.

[00:01:16]This book was my law book, but I'm not um I'm dropping law at the end of this year, you see.

[00:01:24]Cuz I don't enjoy it. I'm not very good at it.

[00:01:54]I have um new notepads coming though.

[00:01:57]So yeah. I'm going to be able to use those, which is going to be nice.

[00:02:08]I did order them to come on Wednesday, but the I don't know what to call it, like a courier, let me down twice.

[00:02:19]But I got my money back, so it's okay.

[00:02:26]Okay.

[00:02:29]So I am doing um Well It's not really homework, it's more just revision, but like the like transformations of graphs and stuff like that, you know.

[00:02:47]So I'm going to basically try and walk you through it.

[00:02:54]Because I heard that teaching is a good way to it's kind of cement that in your own knowledge bank, you know.

[00:03:08]Then again, I don't know it off by heart, so I might have to check.

[00:03:18]I do want you guys to be able to hear this though, that's the thing.

[00:03:22]So Yeah, I think you should be able to hear it.

[00:03:45]Um >> No. Okay.

[00:04:01]So, that is the So, that is the graph That is the curve of x. I don't know if you can do it with a curve. I'm pretty sure you can. I don't see why not.

[00:04:11]Okay.

[00:04:15]So, I'm really bad with graph transformations.

[00:04:21]But, I can tell you the ways you can transform a graph.

[00:04:27]So, there are stretches and I guess What's the other way? What's the other word for like like an inward stretch?

[00:04:41]Like a compression.

[00:04:52]You can reflect a graph.

[00:04:59]And I'm pretty sure that is translate like the same. It means the same thing.

[00:05:05]And the other one, I think, it's just a like move [clears throat] it.

[00:05:11]Do you get this the same, but it's not like flipped and it's not stretched or it's not compressed. It's I don't know what it's called.

[00:05:19]Like like a transformation.

[00:05:22]You know?

[00:05:24]I I'm going to Hold on.

[00:05:26]>> [snorts] >> Okay.

[00:05:28]I used some of my big brain and uh printed out I don't know where my scissors are.

[00:05:40]I thought I had them in here, but How do I do those things so easily?

[00:05:50]I just I I'm sure I had the video, you know.

[00:05:57]Like Sorry. I'm sorry for the hold up. It's not really important.

[00:06:12]It was just going to be a nice trigger for you guys to listen to.

[00:06:17]Obviously somebody didn't trust me with scissors.

[00:06:21]But I printed out this uh this is all of the all of the different functions which I am going to be drawing graphs for to hopefully help you guys.

[00:06:39]First, I'm going to fold it because we love to procrastinate. Let's start.

[00:07:18]All right.

[00:07:19]I'm actually going to keep this because it's going to help me a lot.

[00:07:22]Cuz I'm not the best when it comes to uh graph transformations. Look what I found.

[00:07:42]I suppose to you guys this must seem weird because you usually that I've used in other videos.

[00:07:47]But to me it's just like stuff I have all the time in my room, you know.

[00:07:53]Not the gloves. I don't have the gloves though.

[00:07:56]I just kept those for if I want to make another video with them soon.

[00:08:26]I look so strange right now.

[00:08:31]Okay.

[00:08:35]Okay, back to the task at hand.

[00:08:39]Which is maths.

[00:08:44]Right on.

[00:08:49]So, the word that I was looking for to go here was a translation.

[00:08:59]Which is different to reflection.

[00:09:06]So, that is our function of x curve.

[00:09:11]I know it's mirrored for you guys, but I'm sorry. Okay, I'm sure you can manage.

[00:09:19]So, the first one we're going to be doing is the function of x, which has a translation.

[00:09:31]Um in the y axis.

[00:09:38]Okay.

[00:09:39]So, I'm going to make these graphs a little bit smaller so they can all fit.

[00:10:02]Okay.

[00:10:03]I don't know why I'm showing you that.

[00:10:04]It's not doing anything.

[00:10:10]Let me know how you guys like these longer form videos and if you'd like to see more.

[00:10:16]Um obviously I can't do them every single night because that means I'd be doing like I mean such a big chunk of my life would just be ASMR.

[00:10:26]Um but I don't I mean it's the weekend, you know.

[00:10:30]So, every now and then I don't mind.

[00:10:33]>> [snorts] >> Um and make sure to subscribe if you do enjoy.

[00:11:28]Okay.

[00:11:29]So, here we have our function of x + 2.

[00:11:36]And as you can see, uh the curve interse- now intersects at uh 0 2.

[00:11:45]You see it's moved up two on the y-axis.

[00:11:47]Now, it affects the y-axis because the + 2 has been added outside of the function.

[00:11:55]As you can see, it's added on the end rather than in the brackets.

[00:11:59]So, because of the + 2, the the curve has moved up two.

[00:12:04]And the x hasn't changed because it just hasn't.

[00:12:07]And then, f of x - 2.

[00:12:10]Same pattern. It's moved down two, and now crosses at 0 - 2.

[00:12:16]Which is obviously two less from the origin.

[00:12:20]So, very simple.

[00:12:24]Uh I hope my explaining is okay.

[00:12:28]I I I have lots of notes because this was a law book.

[00:12:35]I still have to continue law until summer, but I don't have to really care about it because I'm not going to do it anymore.

[00:12:43]It's so I stressed out so much about law, you know?

[00:12:47]Now that I'm going to be able to focus more on maths, and I'm going to buy a laptop soon.

[00:12:53]That's the money I have saved up.

[00:12:55]So, we are locking in for second year.

[00:13:06]Okay.

[00:13:09]Next is the the same thing, but it's the translation on the x-axis rather than the y-axis.

[00:13:21]So, for these ones, for these ones, >> Okay.

[00:13:35]Just give me 1 second. Sorry.

[00:13:38]I'm trying. Guys, I'm trying so hard.

[00:13:41]Give me a break.

[00:13:59]Wait, sorry.

[00:14:00]I'm just reading this cuz I have to obviously do the paper.

[00:14:10]That's right.

[00:14:12]Okay.

[00:14:13]So, this one is so confusing. Oh my god.

[00:14:19]Yeah, okay.

[00:14:21]I didn't expect it to suddenly get this confusing.

[00:15:02]Okay.

[00:15:04]So, for these graphs, I mean, yeah.

[00:15:07]Uh these two.

[00:15:09]This is the f x + 2 rather than f x + 2.

[00:15:14]It's f x + 2. You see, it's in the bracket.

[00:15:18]Now, this means that it is a translation on the x-axis, which I already mentioned.

[00:15:25]I think an easy way to remember this is it's in the bracket with the x.

[00:15:30]So, it's on the x-axis.

[00:15:33]Simple enough, right?

[00:15:35]But for some weird reason, even though it's a plus two, it it does the opposite of what you think.

[00:15:44]So, rather than the original graph here moving two to the right into the positive, it actually moves two to the left.

[00:15:53]So, for the fx plus two, it moves two to the left, making its turning point at minus two zero.

[00:16:02]And over here, this one, the fx minus two, its turning point is two two zero.

[00:16:10]See, it's moved over into the positive um What is it? The positive uh like axis area where it has both positive x and positive y, you know, cuz it's like You know what I mean. I'm sure you know.

[00:16:29]Right?

[00:16:30]Yeah.

[00:16:32]Okay, moving on.

[00:16:35]Next up, we have reflections.

[00:16:42]Now, reflections aren't really going to work with a curve which is like perfect like because if it's if it's like that, if you reflect it, it's just going to be like that. So, yeah, that's a pretty tricky.

[00:17:03]I think I'll have to make a new graph to show you guys the reflections.

[00:17:33]>> Okay.

[00:17:49]Yeah.

[00:17:50]So, here is our new function of X.

[00:17:54]It's just over the graph and the curve, which is just here.

[00:17:58]It's well, there.

[00:18:01]Okay.

[00:18:02]So, the reflections, you can have it to reflect on the X axis or in the Y axis.

[00:18:13]Now, if it reflects off of the X axis, that means it's going from here, crossing the X axis and the bottom, making it so that it's like that, it'll be like that.

[00:18:25]I'm pretty sure. I really hope so, otherwise I am Um Yeah.

[00:18:34]Yeah.

[00:18:36]So, minus f of X. The reflections always get me.

[00:18:43]It's that just so confusing, you know?

[00:18:46]And the things like scale factors, just like stop, you know? Stop adding more and more.

[00:18:52]I feel like that's a big problem which happens with the maths.

[00:18:56]It starts out incredibly easy and just spikes It just gets impossible very quickly, too.

[00:19:12]Good.

[00:19:55]Okay.

[00:19:58]So, here is how it looks on my x-axis I showed you.

[00:20:02]This one is the minus f bracket x.

[00:20:07]This one is the reflection over the x-axis.

[00:20:10]So, as you can see, I've done a little um like a Let's call it like a dress kind of thing where it used to be like a little sketchy dotted line.

[00:20:19]Now, it's moved over the x-axis. It's been reflected over the x-axis.

[00:20:24]And as you can see, it's a reflection.

[00:20:26]And I think maybe the only way to remember these two two different differences is that this is a positive x, so it's in the x-axis.

[00:20:38]This is a negative x.

[00:20:41]That seems to be the only logical way to think about it, you know?

[00:20:45]If you can kind of just remember that rule specifically, you'll have no problems, you know? It's a lot That's what a lot of math tends to be.

[00:20:53]Now, f to the minus x, the graph uh that's our graph.

[00:21:02]Wait, sorry.

[00:21:04]I just went into autopilot.

[00:21:06]Uh so, ignoring this, we have our where it used to be. It's been reflected over the y-axis.

[00:21:15]Um and because it's a curve, it looks the same. It's just been moved, really.

[00:21:19]And now it's here.

[00:21:21]But say if this was a line like this, and it got reflected over the y-axis, then it would be like this.

[00:21:30]You see?

[00:21:33]Maybe that's confusing, too. I I'm not a great teacher.

[00:21:37]I'm just trying to learn myself.

[00:21:41]Um so, if I do get anything wrong, feel free to correct me in the comments. You might save me a few marks.

[00:21:48]So, thank you.

[00:21:50]I don't want to say thank you.

[00:21:53]Get back to work.

[00:21:54]>> [snorts] >> Okay.

[00:21:57]Oh, no.

[00:21:59]Okay.

[00:22:00]Next.

[00:22:02]Next up, I think, is the absolute worst one of all.

[00:22:08]Stretches and compressions.

[00:22:13]It's okay.

[00:22:15]Sorry. It's okay, though. We're going to get through this, guys. Me and you.

[00:22:21]That was a hand check. I wasn't touching your face. Don't worry.

[00:22:25]So, first up is the vertical stretch.

[00:22:37]Okay.

[00:22:38]Here we go.

[00:22:41]I'm going to redraw our original function of X graph.

[00:22:47]>> [snorts] >> All right. There you go.

[00:23:00]Just as it was before.

[00:23:02]Sorry if it's a little bright. I'll try it.

[00:23:05]It is daytime over here.

[00:23:08]It's a crisp Saturday afternoon.

[00:23:13]I love Saturdays.

[00:23:18]Okay.

[00:23:19]So, Yeah, okay.

[00:23:31]Sorry, I'm just trying to you know, work this out properly in my head.

[00:23:45]Okay.

[00:24:04]This one is particularly confusing.

[00:24:09]I feel like it's better to Okay.

[00:24:38]So, this is our current This is what I've got right now.

[00:24:41]I have the original function of X.

[00:24:44]And then, I have two other legs here.

[00:24:47]So, I did some vertical stretch.

[00:24:52]That means What does that mean?

[00:25:02]Wait.

[00:25:09]That's so confusing because it makes you think that like stretches and compressions are the same.

[00:25:16]You know, because if there's a vertical stretch, you think that it means up to down, so it's going to go like that.

[00:25:23]But then a compression is going to squash these original curves together, which is going to make it look just like that.

[00:25:33]I'm not crazy.

[00:25:37]This is insane.

[00:25:39]Who invented this?

[00:25:43]What the hell?

[00:25:47]I'm going to watch a quick video to try and wrap my head around this.

[00:25:52]You guys just relax.

[00:25:55]Okay, my crisis is over. I kind of wrapped my head around it.

[00:26:00]I just started crashing out there for a second. Gosh.

[00:26:03]Um okay, so we had this, didn't we?

[00:26:09]We're going to be using a scale factor of two for our vertical and horizontal stretches.

[00:26:15]Now, we need to put into perspective vertical is the Y axis, up to down.

[00:26:21]Horizontal, horizon, left to right.

[00:26:24]Okay.

[00:26:25]So, if you have a vertical stretch, okay, by a scale factor of two, that gives you 2 f of x.

[00:26:36]Every Y value is going to be timesed by two.

[00:26:44]Which means essentially if we have a value here at three three and here at minus 3 3.

[00:26:55]Then this is going to turn into I don't know minus 3 minus 3. This will become minus 3 minus 6.

[00:27:06]That's so confusing. I'm so sorry.

[00:27:08]If this is I'm not a good teacher. If this is 3 3 here, okay.

[00:27:17]After the stretch by a scale factor of 2, it's going to be 3 6 because the Y value has been times by 2, but the X value hasn't changed. So, the graph essentially becomes taller.

[00:27:32]So, although there's no numbers here, I'm going to try my hardest to do this.

[00:27:42]Do you see?

[00:27:44]It's like that.

[00:27:53]>> [snorts] >> Okay.

[00:28:06]Okie doke.

[00:28:08]Now, for the horizontal stretch, now we're going to be using a scale factor of 2 again, except for this one, the number is going to be inside of the bracket with X, just before the X.

[00:28:29]And you'd think that it would be f of 2x, but it's actually f of a half x.

[00:28:38]I don't know why.

[00:28:41]I don't know.

[00:28:42]I don't even know how that would come to that number. Where did we even get that half from?

[00:28:52]Let me Oh god.

[00:28:57]I'm so sorry. I'm This is so confusing.

[00:29:07]Regardless of the numbers though, it works in the same way as the X value is being multiplied by two, I think.

[00:29:22]So, the graph is going to be from this to like this. The graph is getting wider as it's being stretched in the X direction.

[00:29:33]We got this. We got this. We're going to do this. We got this.

[00:29:37]No.

[00:29:41]I don't know why it's the half. The half is what is really confusing.

[00:29:51]We're going to get through this. Okay, we got this.

[00:29:55]I'm so locked in right now. You don't know what I'm doing this stuff. You don't get it.

[00:30:02]Also, once I do this one, we're going on to logarithms.

[00:30:12]I'm going to lock in, guys.

[00:30:15]Okay.

[00:30:16]I'm going to get a few questions up and write them down and we're going to go through them together.

[00:30:20]Questions from my actual homework. It's going to be okay. All right.

[00:30:30]So, if you're asked to sketch the function of X which has been horizontally stretched by a scale factor of two, you What?

[00:30:47]Just what?

[00:30:54]Let me just I'm sorry.

[00:30:58]Okie dokie.

[00:31:00]I'm back.

[00:31:02]So, I I asked um Google a few questions and I came back.

[00:31:09]It's kind of like a weird logic that you need to like sort of compensate by like halving it.

[00:31:17]I think it's just the number in the function that changes though. I don't know.

[00:31:22]I might have to ask my maths teacher about this and see if she can help me.

[00:31:28]I've got some exams coming up and I'm not feeling very good about them, which is why I'm here.

[00:31:34]So, if you guys notice more study videos that might be why.

[00:31:41]Okay.

[00:31:48]Oh.

[00:31:50]There's our graph that has been horizontally stretched by a scale factor of two. As you can see, it's gone wider.

[00:32:00]All of the X values have been multiplied by two.

[00:32:39]All right.

[00:32:40]So, this button with the number being weird for the horizontal stretch for the horizontal stretches.

[00:32:50]It follows whatever So, if the scale factor is three, then it's going to be 1/3. Scale factor is four, it'll be a quarter. So, essentially, when you write out your function, just throw it into the denominator of a fraction of a one.

[00:33:07]And apparently, that works.

[00:33:10]Oh, just to make that simple, I'll just say one over whatever the scale factor is.

[00:33:15]And it's in with the X because it's I mean, you know it's going to be horizontal on the X axis because it's inside the brackets.

[00:33:29]You know, it's with the X.

[00:33:31]Does that make sense?

[00:33:33]I really hope that makes sense because I'm really trying to help.

[00:33:40]And if it makes you guys feel any better, I'm sure this is meant to be difficult.

[00:33:44]Um unless you feel really easy and good about this, then good for you. I don't.

[00:33:51]I think it's time for a little break, though.

[00:33:55]You know, we're going to have some dingle time.

[00:34:02]I got this from a shop small.

[00:34:07]I just can't decide if these hands are too sharp or if they're just right.

[00:34:32]It's like a fidget thingy.

[00:34:36]But then again, I can make keyboard sounds without having to have a full keyboard in my face, you know?

[00:34:53]What sound it was like in right now?

[00:34:55]Kind of.

[00:35:01]By the way, I know Apex is always on there, but it's usually because I am playing Apex and then I remember like wait, I need to make a video.

[00:35:10]I don't I do I do do other things, promise.

[00:35:14]Um I've been really hooked on Apex lately, guys. Very fun at the moment.

[00:35:20]Um I need to play Titanfall.

[00:35:22]It's definitely on the on the cards for the summer.

[00:35:26]If I feel like playing a story game, that's there.

[00:35:31]At the moment, I haven't got time to be investing time into my uh story games and stuff.

[00:35:38]You know.

[00:35:40]By the time you guys are seeing this by two, I think I'm going to be going to the gym.

[00:35:45]Sounds fun.

[00:35:46]Uh I went for I did a 5K this morning, too.

[00:35:51]Very productive of me, I know.

[00:35:56]It's nice to feel productive.

[00:36:01]But you know what's even nicer?

[00:36:05]Having a nice sleep and relaxation.

[00:36:09]So.

[00:36:11]That's your current task.

[00:36:20]Just relax.

[00:36:27]I do want to get a good photo for the thumbnails of my but then again I mean how good does a thumbnail get, you know?

[00:36:41]Normally, I just put when I'm putting the videos together, I'll just go through and look for something that makes me think like, yeah, that'll do, and then I just make it the thumbnail.

[00:36:54]I changed yesterday's logo because everyone was like, the smile is creeping me out.

[00:36:59]>> [laughter] >> Which um I did when I took that photo, I thought people might either say might find it like strange because I was laughing when I did it. Um or people would be like, oh, I I clicked because the smile is so cute, I don't think.

[00:37:20]Um but I changed it anyway, and it didn't really matter. Nobody really cares that much.

[00:37:40]So, wherever you guys are in the world whether it's one of the seven continents whether it's my continent, my country or far away in I don't know, Argentina or like Paraguay.

[00:38:01]We did a geography quiz yesterday with those South American countries.

[00:38:04]Uh Ecuador, Peru, Chile Brazil, Colombia um I know Rio isn't country.

[00:38:24]It's I believe it's it's not the capital of Brazil, is it? Because I think Brasilia is the capital of Brazil. It's a city in in Brazil.

[00:38:31]And it's where the Christ the Redeemer statue is, and it's very beautiful.

[00:38:36]Uh we learned about it in geography a couple years ago about like all the different things in there, like favela and stuff, and the Olympics too, and stuff like that.

[00:38:50]It's really interesting, and I love I'd like to go one day.

[00:38:54]I probably not do the dangerous parts though, because I've heard that you know, it it can be dangerous.

[00:39:00]So, everybody stay safe if you happen to be in those dangerous areas.

[00:39:16]All right. Okay.

[00:39:18]Now.

[00:39:21]Now now now now now now now now now now Now, I'm going to get a couple questions from my book of Oh, I just got an email off Amazon.

[00:39:33]On my notepad.

[00:39:34]I'm going to get some questions out of the book, and we will do them, and then I'll finish with some fun tickles. So.

[00:39:43]I'll be right back.

[00:39:46]Okay, guys. So, I've wrote five of the questions down onto the booklet.

[00:39:53]The first one is uh the curve has equation Okay.

[00:39:58]The curve has the equation y equals bracket x plus a all squared.

[00:40:05]So, firstly, we know that an x squared is just the default curve, which would look like that, crossing That's not great, but crossing at the origin or turning at the origin.

[00:40:22]Um So, this is you can pretty much that doesn't really matter as the that just means it's a curve.

[00:40:30]So, basically what we have is a y equals f x + a.

[00:40:38]>> [clears throat] >> And we know that this is a translation.

[00:40:44]Um this is So, let's say this was + 4.

[00:40:48]We know that because it's in the brackets, that means it's on the horizontal, so it's a horizontal translation on the x axis.

[00:40:58]If this was a + 4, you know, we we do the opposite of what we would expect, making it a minus four. So, it's currently going to be x + a, so it'll be x and then a minus a, meaning it would be moved over to this side.

[00:41:17]Is this one where it is moved up a values, which isn't true.

[00:41:24]It's one where it's moved to the right, it's not true.

[00:41:28]It's one where it's moved down, it's not true.

[00:41:31]And the one where it's moved to the left a unit, which is the correct one.

[00:41:40]Took too long to do that.

[00:41:45]So, number two, describe the transformation of y equals ln x onto curve y equals 2 ln x.

[00:41:56]So, anyone that doesn't know, ln is like a mathematical term, similar to Well, actually I was going to say like pi and e, but they both have values. I don't think ln has a value.

[00:42:12]Oh, doesn't?

[00:42:13]Actually, I think it does. Learn essentially means log to the base e.

[00:42:19]That's what that means.

[00:42:21]So, I think it does have a value, but its value isn't important.

[00:42:28]So, essentially, what we have is We're going from y = f of x to y = 2 f of x, I believe. So, that is this is what we had originally.

[00:42:46]This is what we're moving on to.

[00:42:49]Now, is it a >> [clears throat] >> Wait, I can't even remember.

[00:42:58]So, as we know, this means it's stretching.

[00:43:02]And because it isn't with the x, it is in the vertical direction.

[00:43:08]Or the on the y-axis, which is the vertical direction.

[00:43:12]I can't remember.

[00:43:14]Vertical like that, easy way to remember it. Horizon is left to right.

[00:43:19]Horizontal just like that, same thing.

[00:43:22]So, as we know it's a stretch, we can immediately rule out these two.

[00:43:28]Then we have the stretch by a scale factor of two, which is the vertical one.

[00:43:34]Or obviously stretch by a scale factor of half horizontal, which it would be if it was y = f 2x in the brackets.

[00:43:43]So, we can cross that one off.

[00:43:45]Sorry.

[00:43:47]And we know it is the vertical stretch by a scale factor of two.

[00:43:52]Right.

[00:43:53]Number three I did on my own because it was way too much for me to just write down.

[00:43:58]Um So, I'll move straight on to number four.

[00:44:02]So, the curve y = root x is translated onto the curve y equals root x plus four.

[00:44:10]Now, this one confused me at the beginning cuz these are all vector translations.

[00:44:17]But, a good way to look at it is the top number is just the like number of units moved on the x-axis and the bottom is number of units moved on the y-axis.

[00:44:30]So, just think about it as you know, when we write down coordinates, we write it as x y.

[00:44:36]X is first, y is second. Easy peasy.

[00:44:40]Okay.

[00:44:40]So, after looking at this, I realized what it was essentially asking me is to say what translation would be required to go from y equals f of x to from y equals f of x y equals f of x to y equals f of x plus four.

[00:45:00]That's essentially what it's asking.

[00:45:03]And as we know, the this means we would move four units to the left on the x-axis as it's in the brackets with the x.

[00:45:14]So, this will be opposite. So, rather than adding four to go right, it would take away four to go left on the x-axis.

[00:45:25]And so, I can cross this one off. Oh, actually, it's a circle, which would mean this one minus four on the x and don't change the y.

[00:45:35]That one is the right answer.

[00:45:39]See, all of this makes so much sense when I do it like this.

[00:45:42]Now, the final question. There was 15, but I wasn't going to write 15 questions. I decided to just do five.

[00:45:48]Stretch y equals ln x with scale factor two.

[00:45:53]So, once again, I've basically said let ln be f.

[00:45:57]I did it wrong.

[00:45:58]I'm They're not equal to each other.

[00:46:01]But, I'm letting the lin equal f.

[00:46:05]So, it could be like y equals f of x.

[00:46:11]It's like that.

[00:46:13]>> [snorts] >> Except this this would be lin, you know?

[00:46:17]Now, this one really did confuse me at first.

[00:46:22]I think it said horizontal.

[00:46:24]Actually, it did say horizontal cuz otherwise this isn't specific enough.

[00:46:29]Um so, if this is a horizontal, we know it's on the x-axis. So, rather than with the scale factor being a two, the scale factor is going to be 1/2. So, we can already rule out this answer and this answer, which leaves us with y equals a half lin x or y equals lin x over two.

[00:46:52]So, uh I originally got this one wrong, but then realized my mistake.

[00:46:57]So, here, we would essentially be saying y equals Sorry, it's difficult.

[00:47:09]I'm like writing through my phone. We'd be saying y equals half f of x.

[00:47:14]Whereas here, we're saying y equals f half x. It's like that.

[00:47:30]And as we know, this stretch would be a >> [clears throat] >> vertical stretch as it's outside of the brackets.

[00:47:38]Whereas this stretch is horizontal because it's in the brackets with the x.

[00:47:44]So, if my maths is not mistaken, that means this is the correct answer.

[00:47:55]Okay, guys, I'm back. Hello.

[00:47:59]Now, I think it's time to say that study time is over for today.

[00:48:06]>> [snorts] >> It felt good to go back over that, you know.

[00:48:14]Now that it's nice, fresh in my brain.

[00:48:17]Hopefully, every time I think about it, it'll get easier and easier until it goes into like long-term memory.

[00:48:26]And then I don't have to remember it. I just know.

[00:48:31]Okay.

[00:48:33]Okay.

[00:48:34]Okay. Okay. Okay.

[00:48:36]I am going to do you some tingles now.

[00:48:43]Some tingles. Some tingles. Some tingles. Tingles. Tingles. Tingles.

[00:48:46]Tingles. Tingles.

[00:48:48]Because we had a good study session and we actually got quite a bit done.

[00:48:53]I know that's it's kind of simple, but it's something that is important to know and understand.

[00:49:02]And we got to kind of brush on logarithms, but not really.

[00:49:06]Logarithms are more like So, instead of having like x to the power four, you would have like four to the power x. So, when you don't know what the power is, you use logarithms to work it out.

[00:49:23]But really, I really need to go back over those logarithms because they are pretty confusing.

[00:49:35]Lucky dogs.

[00:49:40]God, it's nice to hear all this tapping again, you know.

[00:50:08]>> Oh.

[00:50:14]Why does everything smell so weird?

[00:50:17]There's a little leaflet in my water bottle.

[00:50:21]Hopefully it's like a treasure map or something. Cool.

[00:50:44]I think you don't really realize how long an hour is until you're making an ASMR video.

[00:50:49]And then all of a sudden it's like whoa.

[00:50:52]You want me to just tap on things for an hour?

[00:50:59]But I mean I don't I don't hate ASMR. Obviously I love ASMR. I love making it.

[00:51:04]>> [clears throat] >> Oh my god, a lot of work to do.

[00:51:18]You know, look at all this work we good guys.

[00:51:26]Trying to get a good thumbnail.

[00:51:34]I'm so happy.

[00:51:36]I don't know. I don't know why I'm even happy.

[00:51:40]I love being able to make these videos and I love like the fact that you guys genuinely enjoy them is just so awesome because I spend a lot of time doing them, obviously.

[00:51:53]And seeing like a a nice reception just like it's just like oh You guys, come on, man.

[00:52:03]I love it.

[00:52:10]Just say oh.

[00:52:13]Halfway through the video.

[00:52:15]And if you made it this far, you deserve a medal.

[00:52:18]Congratulations.

[00:52:20]If you're still awake cuz it's pretty relaxing, are we?

[00:52:25]Make sure to subscribe. Subscribe, subscribe, subscribe.

[00:52:42]It feels really cool to make longer videos because it's like it feels less like I'm just recording and more like I'm like hanging out, you know, like it's like a hangout.

[00:52:51]Even if it's just me on my own. You guys are there in spirit. And when you see this, it's like you're hanging out with me.

[00:53:00]Everybody wants to hang out with me, dude.

[00:53:04]I'm just kidding.

[00:53:08]It feels good to do the homework you've been meaning to do, you know, the thing you've been dreading.

[00:53:16]Once it's out of the way, you just get to be happy.

[00:53:20]And when I get my uh laptop, which I've been saving up for I'm going to be able to do a lot of work with it.

[00:53:29]Which I can't do when I have no notebooks, you know.

[00:53:34]Uh This doesn't sound quite crisp. Crisp. crisp, crisp, as I wanted it to.

[00:53:50]As I think there's quite a metallic sound to it.

[00:54:00]But it's still not bad.

[00:54:06]I'm doing it far away so it's not too loud for you guys.

[00:54:11]Oh, yes.

[00:54:13]Fine. I've got a tennis racket here which I used a few videos ago.

[00:54:19]And I thought I haven't used that in a little while. I should I should get back on that.

[00:54:36]So if you haven't already relax, get into bed.

[00:54:44]Try to now close your eyes.

[00:54:50]Just focus on my voice and the sounds coming out of my tennis racket.

[00:55:07]Fortunately I trimmed my fingernails meaning I think I did it on the video actually but my tapping game is still out.

[00:55:15]It's coming back though.

[00:55:18]Soon enough guys, soon enough. Don't worry.

[00:55:25]We are nearly at 2,500 subscribers.

[00:55:32]So cool.

[00:55:36]The growth is steady, but awesome because you know, like I still find it exciting to check YouTube studio and be like, "Oh, I wonder if like I wonder if I've gained which may be sad a little bit, but I'm not like I guess that's kind of like on level of googling yourself.

[00:56:02]But, I'm just checking up on how things are going, you know, and if it shows me comments, which YouTube might not always notify me of.

[00:56:28]Oh.

[00:56:30]I like that.

[00:56:33]I don't know what I'm going to do with him.

[00:56:35]Probably arms.

[00:56:40]You know I love arms.

[00:56:43]I know you guys love my arms, too.

[00:56:46]But, um maybe not. I might do like chest or back or something. I hate back. Back is so bad because it just hurts my hands so bad, the calluses.

[00:57:00]That's why I don't do back very much.

[00:57:04]I really I shouldn't do because back muscles are like pretty cool, you know.

[00:57:13]Okay, Rafael out.

[00:57:15]He's here. He just tends to watch me sleep.

[00:57:49]>> It kind of sounds like a horse galloping if you listen and imagine.

[00:57:58]I always suspect a nice like >> [panting] >> You know what I mean?

[00:58:04]They do that thing with their mouth.

[00:58:08]I don't know. Never mind.

[00:58:25]I'm going to put this on book which I have from yesterday.

[00:58:29]I don't I I have one left over. I'm going to put it inside of a whale.

[00:58:33]It's like a little mystery treat so next time I record with him uh I'll get a nice surprise.

[00:58:42]So stay tuned if you want to see me be like, "Oh, yeah."

[00:58:47]Cuz I will forget like very quickly, I promise.

[00:58:54]It's funny how our mind works like that, you know? You just forget things.

[00:59:02]I'm a pretty forgetful person, too. I forget like things that I shouldn't forget.

[00:59:08]I remember all the important things, too.

[00:59:18]Okay, everybody.

[00:59:20]Thank you very much for joining me this afternoon on our long long study session.

[00:59:30]Thank you for being here with me.

[00:59:32]I hope I hope I was able to relax you.

[00:59:39]Let me know how you like this new trigger.

[00:59:42]I'll see you a lot more of it.

[00:59:47]Hit that subscribe button.

[00:59:49]Thank you for watching.

[00:59:51]And I will see you very very very soon.

[00:59:58]Bye-bye.