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For more information, please see full course syllabus of AP Calculus AB
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Desmos Tutorial

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Desmos Tutorial 1:42
    • Desmos Tutorial
  • Things You Must Learn To Do on Your Particular Calculator 2:39
    • Things You Must Learn To Do on Your Particular Calculator
  • Example I: y=sin x 4:54
  • Example II: y=x³ and y = d/(dx) (x³) 9:22
  • Example III: y = x² {-5 <= x <= 0} and y = cos x {0 < x < 6} 13:15

Transcription: Desmos Tutorial

Hello, welcome back to, and welcome back to AP Calculus.0000

In this lesson, what I thought what we would do it is a desmos tutorial.0005

I have talked about the software that I use to draw out the particular graphs that I do.0009

I thought I would show you real quickly how to use.0013

It is very simple but the truth is you do not really need this tutorial.0016

But I will just give you a nice brief breakdown of how to enter the function,0021

how to graph, how to zoom, how to set the window, and things like that.0024

Before we start that, I did want mention to mention though,0028

for this particular course, you are going to have a graphing calculator.0033

In fact, it is going to be required for the AP exam.0036

Part of the AP exam is going to be taken with a calculator.0039

Anything that we do that I use desmos for, to demonstrate for you guys,0042

you want to learn to do on your calculator.0047

What I decided is, I will do the desmos tutorial.0051

I think it is important that you guys actually learn how to use your particular calculator.0053

Most of you are going to have a TI 84 or 84+, or 84 Silver Edition.0058

Essentially, it is just a TI 84, but some of you may have other calculators.0064

Instead of me doing a tutorial on how you should use your calculator,0070

what I will do is I will go quickly through what it is that you need to be able to do on your calculator.0075

And then, I'm going to leave it to you to actually go to the guidebook, it is available online.0080

I will show you here and learn how to use it yourself.0087

I think that is an important part of it, going through a technical manual0092

and learning how to use your particular calculator and getting used to it, as opposed to having me show you.0096

In any case, let us talk about the calculators.0103

You are either going to have a TI 83, you are going to have an 83+, or an 83+ Silver Edition.0105

Probably, not going to see too many of those.0115

Most of you are going to have the 84 or the 84+, the TI.0117

This should not be 43, this should be 83.0122

The TI 84+ Silver Edition, some of you might have the TI 89.0128

Essentially, what you are going to do is you are going to pull up in a Google search, TI 84 guidebook.0134

Of course, all of these links are going to be down below in a quick note section for you, if you want to do that.0141

Or you can Google search it yourself, it is not a problem.0145

Just pull it up, download it, or open it, you do not have to download it,0149

if you do not want to, and learn how to use your particular calculator.0153

The things that you are going to have to learn to do on your calculator are the following.0158

You have to learn to graph a function, very straightforward.0162

Graphing a function and its derivative in the same window,0167

whether it is first derivative, second derivative, things like that.0170

Zooming in and out, you are going to have to be able to adjust the viewing window0174

because you have to go to different parts of the graph.0178

You are going to have to use the table of values that accompany the graph of a given function.0181

You have to be able to know how to read the table of values.0186

How to actually change the table of values and things like that.0189

Let me check these off as I go, zoom in and out, adjusting your window.0194

You have to learn how to calculate the derivative of a function at a point, that is going to be important.0200

You are going to have to learn how to calculate the integral of a function over a particular interval.0205

You have to learn to calculate max and min values on your calculator.0213

You have to learn how to calculate the roots of a function.0216

Given a function, where does it cross the x axis, that is all the roots means.0219

Changing between degree and radian mode.0225

That is pretty much it.0227

It is not a lot, you can actually probably knock out all of these.0229

Probably within 1/2 hour or maybe 45 minutes.0233

Just might have to jump around a little bit in your particular guidebook.0236

But the guidebooks are reasonably straightforward.0239

They tell you everything you need to do, all the buttons you need to press.0242

Just practice with it, play with it, and get used to it.0247

These are the things that are going to come up.0250

They are not going to come up all at once.0252

For example calculating the integral of the function.0253

You know you are not going to need to do that until the second semester.0256

But most of the other stuff, roots of a function, changing the degree in radian mode,0260

adjusting your viewing window, these are all really basic things.0266

Again, all of this together should not take you more than about half an hour or 45 minutes.0270

With that, let us go ahead and jump right into desmos.0275

I want to teach you how to use that.0278

When you do your homework, you can even use your calculator.0280

It is a great way to get used to it or you can use the desmos.0283

Again, my particular preference is the desmos, it is wonderful.0286

On your test, it is going to be calculator.0289

You are not going to be allowed to actually use desmos.0290

Let us get started.0293

Again, it is really easy.0294

When you pull up, as you see up there in the url,0298

you are going to get this window and it is going to be this big red button.0304

It is going to say launch calculator.0307

Click the button and this is what you see.0309

This is the screen that you see.0312

This box is right here.0315

These boxes in blue, it is going to be different colors.0318

Blue, purple, red, it is sort of random.0321

Those are where you are going to enter your functions.0324

Let us start with a particular function.0327

You can do y =, let us say we are looking at a sin x function.0330

You just enter it, y = sin x, then it comes up.0335

This is the normal what you see.0340

Now let us start doing some things to it.0343

A couple of things that we can do to it.0346

You notice this little pad down here.0347

You can either enter the numbers with your mouse.0351

Here are some symbols for you, if you want.0355

This one right here is probably going to be the most important window.0358

If you happen to you it, these are the functions.0360

Trig functions, statistical functions.0364

It is absolutely wonderful, it does everything, miscellaneous.0368

Probably, the most important thing you are going to use is this ddx 1.0371

That is about it, because you going to take a function and you are going to graph its derivative on the same window.0374

We will do that in just a minute using this ddx function.0381

But before we do, I click it again to get rid of it.0384

Let me talk about these things up here.0387

When you click this little crescent wrench, you are going to get some choices as to what is that you can do.0390

The most important is going to be changing your x and y axis.0397

Now this + and -, simple, it just allows you to zoom, zoom in and out.0401

If you place your mouse on the graph and just trace off the graph, notice that you basically get the different values.0410

At -5.82, the y value is 0.447.0419

These are radian values.0423

It is really nice.0427

Again, this is you zoom in, this is you zoom out.0429

Let me pull that back.0436

This just allows you to change your window, if you want.0440

For example, right now instead from -10 to 10 and the y axis is -12.26 to about +12.26.0444

A nice basic square thing.0453

If you want to, just click on it, type -1 and click on it over here.0456

Let us do maybe 7.0465

Now it gives me from -1, as you can see, to 7.0467

You can change the y, let us change the y, let us make it -2.0472

Over here, the upper one, let us go ahead and change that let us say 6, something like that.0480

Again, you can get rid of calculator just by clicking double x.0488

That is really about it, this is really all you need to know.0492

You need to be able to graph your function.0495

You need to be able to zoom in on your function to find out a particular value and that is essentially it.0497

Let us go ahead and talk about this little thing up here.0504

When you click it, what it does is it gives you some options.0507

The most important option is this thing.0511

Notice it says convert to table.0513

What it will do, it will convert your function to a table of values.0515

When I do that, there you go.0520

I see my function up here, sin x, and I see the different values.0522

You can plug anything you want.0528

If I put my cursor there and if I can get rid of all of them, and I can plug in whatever value I want.0529

Let us say I want to find the sin(47).0537

I do 47, I hit enter, the minute I hit enter it just gives me another line.0539

35, -25, this is really a fantastic tool.0545

I got myself the graph, I got myself a table of values.0552

I can work as I see fit.0557

When I click that little arrow, it goes away.0563

Now let us enter a function and its derivative on the same graph.0566

I’m going to pick a function like, let us say y = x³.0571

Again, you enter it with x and the little caret symbol, cubed.0578

Notice where the cursor is.0582

Once I hit the caret symbol, the cursor is still in the exponent.0584

To drop it back down to the normal line, you just hit the right arrow.0588

When you hit the right arrow, either here or on your keyboard, and drops it there.0593

As you see, the minute you enter it, the graph shows up.0600

Now when I hit enter, it gives me a new line.0604

Notice that this particular graph is in red.0606

I will show you in a minute how to change the color.0609

There are a couple ways that I can do the derivative.0612

I know what the derivative of x³ is, it is 3x².0615

I can either just enter y = 3x², let us try that.0619

y = 3x², right arrow.0624

Notice it is in blue, I'm going to get a nice blue graph.0630

The red is my function, the blue is my derivative.0633

I think what is nicer is to, let us go back here, let us do y =,0638

Let us go to the function screen.0646

Function, and again, ddx.0647

I go up here, and with my cursor, I copy this.0652

Once I copy it and I come back here, I put a little open parentheses and I paste it there.0659

Now this is telling me I have my y = x³.0668

I have my y = ddx of my x³.0673

In this particular case, if it is a complicated function, you do not know the derivative but you want to see the graph of it.0677

You can use this ddx function.0682

It will just take the derivative and graph it for you.0684

It is really fantastic.0687

In this case, it did it in green.0689

If I wanted to change the color, very simple.0690

I click on this and I hold it.0693

There we go, if I click on the color and if I hold it, it will give me some choices.0704

I can do solid, I can make it dotted, let me go back to solid for the original function.0709

I can make it purple, blue, green, orange, black, whatever I want.0716

Let us go ahead and leave that one.0721

Let us go ahead, if I click it quickly, it makes it go away.0723

If I click that, it is giving me a little bit of trouble here.0731

But you saw among the go.0734

We would not worry about that.0744

Just know that if you click it and hold it, basically, it gives you a choice of changing the color.0745

The last thing I think that I want to show you, you got the zoom feature.0751

You can zoom in as much as you want, as close as you want.0758

You can find values, you can highlight a particular equation.0764

You can convert it to a table, look at your table of values.0773

This is absolutely fantastic.0777

You can trace on here to see what the values are, the given x value.0780

The last thing that you want to be able to do on here is to represent a piece wise function.0785

Let us talk about how to do that.0792

Let me do an x and x, clear those out.0794

Let us do a couple of piece wise functions.0797

Let us say from -5 to 0, I have the function x².0799

I enter the y = x², right arrow.0807

That gives me my x² function.0812

Now if I want a piece of it, piece wise.0813

What I do is I put it in braces.0816

In braces, I have to tell myself, I write my interval.0821

x greater than -5 or from -5 to 0.0829

I will write something like this.0834

I will write -5, I can use symbols here.0835

-5 is less than or equal to x, then less than or equal to 0.0842

There you go, it gives me a piece of it.0851

I can hit the right arrow again to take it outside, there you go.0854

That is how you do a piece wise function.0857

You write the function itself, open braces, and then you specify the interval.0860

You can write x less than a number, x greater than a number.0863

In this particular case, x was between two numbers.0866

For the next function, let us say from 0 to 4, let us say something like that.0869

Let me hit enter.0876

From 0 to 4, let us do cos (x).0877

Let us do y = cos(x).0884

Now we will do a brace, can we do it here.0890

Let us do x between 0 and 6.0903

Again, you have a choice, less than, less than or equal to, does not really matter.0914

Less than x, less than 6, there you go, something like that.0917

That is how you do piece wise functions, just using the braces.0926

That is really all essentially you are going to be using this for.0931

How to do a function, how to graph a function, as far as finding the root of the function.0935

That is really easy, just read it right off the graph.0939

If you cannot read it off the graph, just zoom in until you can.0942

That is it, here you go.0946

Just it click down and it is going to say π/ 2,0.0948

In this case, your root at 0 is π/2, for this particular function.0951

That is it, finding the root of a function, graphing the function, graphing the derivative.0955

Again, when you graph the derivative, you just use this derivative function right there.0960

Zooming in, changing the window, zoom in and zoom out.0966

This little default zoom, when you click that, that just takes you to back home.0970

It takes you back to the beginning.0977

This little crescent wrench allows you to change the x axis and the y axis.0980

That is really about it.0988

Other than that, again, these things over here,0990

when you click on the little color here with the symbol for the graph, it gives you a choice.0993

You can change it to dotted or leave it that way.1000

Or you can change the color of it, orange and black.1004

Let us do black and then just click that.1006

You can change the color as you need to.1009

Let me see, is there anything else that you really need?1013

Not really, now you know how to do roots.1015

You know how to select, highlight it.1018

I have two equations here.1020

Let us say I highlight the second one.1021

I click that thing and I convert it to a table.1023

It will give me a table values.1027

And of course, you have a choice.1029

Just do that, delete, and you can enter whatever value you want.1031

Once again, it will give you, whether it is undefined, or 2, whatever it is.1036

You can set your values.1042

Notice in this case, 56 is undefined.1045

It is not undefined for the whole cosine function.1047

It is undefined because here our cosine function is only from 0 to 6.1051

That is why it tells me it is undefined.1054

You do not have to worry that there is actual problem.1058

Other than that, I cannot really think of anything.1060

Again, you can use this calculator for entering symbols.1063

Here is the x and the y variable.1066

If you need other variables, you can go ahead and click that.1068

You can go back to number.1074

This a, b, c, will give me a bunch of things.1075

Other variables, we have the braces here if you want.1080

Some brackets here, subscript, symbol.1083

If you want to use subscripts, going back.1086

Again, you really only going to be using this ddx function.1089

In case you want, you can use the exponential function, anything you want here is absolutely fine.1093

It is all very intuitive and this is a wonderful tool.1099

I use it all the time.1102

In fact, I did not even use my professional mathematical software anymore.1104

This is pretty much what I use.1107

It gives me everything that I need.1109

Give it a shot, play with a little bit, enjoy it.1112

It is really a lot of fun to use, that is about it.1115

Thank you so much for joining us here at

We will see you next time, bye.1122