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Graphing Calculator Basics

  • Try to flip through through the manual at some point. You don't need to read it carefully, but it can help just to have a sense for what your calculator can do. Then, you can look things up later when you need to know them.
  • Syntax is the arrangement of numbers and symbols to make meaning. Syntax is absolutely crucial with calculators. Your input might look like something to you, but your calculator "reads" it completely differently. Anytime your input might be misinterpreted, use parentheses. By carefully using parentheses, you can tell the calculator what order operations should occur in and how things work. Along those lines, think about the results your calculator is giving you. Try to figure out if it's plausible for them to be correct before automatically believing in them. If something smells fishy, double-check your syntax.
  • For the most part, you'll almost never need to change the settings on your calculator. The only settings you'll definitely need to care about are what unit angles are measured in (degrees, radians) and the graphing mode (function, parametric, polar).
  • Occasionally something will go wrong and your calculator will give you an error message. If that happens, don't panic: read the error message carefully and think about whatever you just did. Usually you'll be able to figure out what went wrong and fix it. If you still can't make any sense of it, just do an internet search. Type the product name of your calculator and what the message says into a search, and chances are you'll have it figured out and fixed in no time.
  • Your graphing calculator is, without a doubt, so much more powerful than you currently realize. Basically, if you come across a new topic, chances are your graphing calculator already has some functionality connected to that topic. Just do an internet search with the product name and the topic you're interested in.
  • The easiest way to learn how to use a new graphing calculator is just to play around! Be curious, try new things, and see what happens! Exploring on your own will do you a world of good. So, go crazy! Explore, play, learn!

Graphing Calculator Basics

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
  • Read the Manual 0:06
    • Skim It
    • Play Around and Experiment
  • Syntax 0:40
    • Definition of Syntax in English and Math
    • Pay Careful Attention to Your Syntax When Working With a Calculator
    • Make Sure You Use Parentheses to Indicate the Proper Order of Operations
    • Think About the Results
  • Settings 4:58
    • You'll Almost Never Need to Change the Settings on Your Calculator
    • Tell Calculator In Settings Whether the Angles Are In Radians or Degrees
    • Graphing Mode
  • Error Messages 7:10
    • Don't Panic
    • Internet Search
  • So Many Things 8:14
    • More Powerful Than You Realize
    • Other Things Your Graphing Calculator Can Do
  • Playing Around 9:16

Transcription: Graphing Calculator Basics

Hi--welcome back to Educator.com.0000

Today, we are going to talk about graphing calculator basics.0002

First, if your new graphing calculator comes with a manual, just take a look at the thing.0005

Now, I don't mean that you have to try reading the whole thing in-depth.0010

Just skim it and get a sense for how things work and what your new graphing calculator can do.0014

You don't have to understand everything, right from the beginning; but you want to know enough0019

so that you can come back later and find something that you are looking for.0023

You are just looking to pick up a sense of how the graphing calculator works.0027

If your calculator did not come with a manual, that is OK; just play around and experiment.0031

You will learn how it works by just trying out new things.0036

In English, syntax means how words and symbols are arranged to create meaning.0041

In math, it is the same thing: it is how we arrange numbers and symbols to create meaning.0046

For example, we could write 45 divided by 32 times 5 like this,0052

and we would be saying the number we obtain from dividing 45 by the product of 32 and 5.0058

If we wanted a calculator to find the answer for us (which happens to be 1, by the way),0064

we might be tempted to enter the following: we would use this as our syntax for putting it in into our calculator:0068

however, if we did that, we would actually get 25, which is completely the wrong thing.0076

Why? because it interprets the above as if we had meant 45 divide by 32, times 5.0081

And by the way, if you haven't seen this symbol right here, it is called a carat.0086

And what it means is "exponent"; so if we write 37, that means 3 to the 7, when we are used to seeing it.0090

On lots of calculators, though, it can't actually raise the numbers at all.0099

So, we end up using a carat to symbolize that the next thing is an exponent.0103

However, what it means by "next thing" is really only the very next thing.0107

So, when it sees this, it sees this as 45, divided by 32; but now we have completed what we are dividing by.0112

And so, it moves on to times 5; so the syntax really matters--how we set things up specifically with symbols.0119

This illustrates just how important it is to really think about the syntax we are using with a calculator.0127

Make sure to use parentheses to indicate the proper order of operations.0132

How you want the calculator to do things--you have to tell the calculator with syntax.0136

So, if we want to have 45 divided by (32 times 5), what we do is say it as 45 divided by...0141

and then we will put quantity (32 times 5); that way, it knows that it is being divided by the whole thing of 32 times 5.0147

Any time that your input might be misinterpreted, use parentheses.0156

It never hurts to have unnecessary, extra parentheses; putting in too many parentheses doesn't actually do anything bad.0162

But oh, how it can hurt if you miss putting them on an important problem.0169

So, you are better safe than sorry; if you think it is possible that the calculator won't know what order you want things to happen in,0172

put in parentheses to make it absolutely obvious which one you intend.0178

For example, with this, the 32 * 5, 3 exponent 2 times 5, we might be worried that it is going to interpret it as 3 exponent (2 times 5),0182

so 310; so we might want to put (32) in parentheses, as well, and then multiply by 5,0191

that whole thing in parentheses; and we are dividing 45 by that whole thing.0198

Now, as you work more with your calculator, you will start to get a sense for exactly how the syntax works.0201

And you would realize that it only interprets the very next thing as being what the exponent is.0206

So, I will be safe with just 3 exponent 2 times 5; it will interpret that as (32) times 5.0211

But it takes a little bit of a while to figure out exactly how it works.0218

And once again, you are better safe than sorry; more parentheses are always a good thing if you are not sure what it is going to have.0221

So, along those lines, think about the results that your calculator is giving you.0227

You don't want to just blindly assume, "Because my calculator told me, it has to be right!"0231

You want to try to figure out if this is plausible--if this is vaguely reasonable for me to get these numbers out of it.0235

If we did 45, divided by 32 times 5, and it came out as 25, we should think,0241

"Well, 45 divided by at least 9...45 divided by something around 10...that is going to be much less than 25"; so it sets off an alarm bell.0245

We might not know what the answer is going to be beforehand, and we shouldn't (why would we be using a calculator if we did?).0253

But we have a sense of a big range of what we should expect.0257

Should it come out positive? Should it come out negative? Should it be hundreds? Should it be thousands?0262

Should it be a single-digit answer? Should it be small decimals? What is going to happen, in a vague sense?0267

That way, if something goes horribly wrong, we will think, "Oh, something is weird here."0273

So, try to figure out what will be a plausible answer before you just punch it in and automatically believe what you see come out of your calculator.0277

And if you end up seeing something that seems a little bit strange--it "smells fishy"--double-check your syntax,0285

and make sure that you told the calculator what you meant it to do,0290

and that you didn't accidentally tell it something slightly different from what you wanted it to do.0293

For the most part, you will almost never need to change the settings on your calculator.0298

Pretty much all of the settings on your calculator, you will be able to just leave as the factory standards.0302

There are some that you might occasionally want to change; but that is probably sort of an advanced user thing0306

that you won't really need to deal with for many years.0311

The only settings that you will definitely need to care about for the next couple of years are what unit angles are measured in, and the graph mode.0313

Other than that, you are basically fine leaving all of your settings the same.0321

The calculator has to be told in the settings about angles, though.0325

It has to be told whether the angles you are working with, the angles you are giving it0328

(and this is for trigonometric functions) are in radians or in degrees.0332

If it is in the wrong one, if you mean to do your problem in radians, but you accidentally have it set in degrees, you are going to get completely wrong answers.0336

So, it is really important that you know which one it is in, and that you have it set in the correct one.0344

It is normally a pretty easy option to find and change whenever you need to.0348

So, whenever you switch from radians to degrees, make sure to think, "Oh, did I go and change it in the settings?"0353

Also, one way to double-check which one you are in is to do something like sin(π/2) or sin(90).0358

Sine of 90, if you are in degrees, will come out as 1; sine of 90, if you are in radians, will come out as not 1;0366

and you will immediately know if you are in radians or degrees by just putting in this simple number, sin(90).0372

It will tell you which one you are in without having to check the settings.0377

But it is also normally really easy to check the settings; it is just a single button-press.0380

Be careful when you are swapping between radians and degrees; make sure you are using the right one,0384

because if you aren't, all of your answers are going to end up coming out wrong.0387

The other thing that you have to care about changing is the graphing mode, and that is similarly easy to change.0390

This allows you to switch between function, parametric, and polar graphing modes, and sometimes other graphing modes, as well.0396

But those three (function, parametric, and polar)--those are the really important ones that you want to know about.0402

Normally, you will want it in function mode most of the time; and so, that is what we will be talking about first.0407

But we will talk about the other ones later, in the last lesson of this appendix.0412

We will talk about parametric and polar for a little bit.0417

But normally, most of the time, you will do all of your work in the function graphing mode.0419

And that is what you want to usually leave it in.0423

Occasionally, something will go wrong, and your calculator will give you an error message.0426

If that happens, don't panic: you can figure out most error messages, simply by reading them and thinking about whatever you just did.0430

Try to get a sense of what this kind of means, and then ask, "What did I just do with my calculator that might have caused something to go wrong?"0438

Thinking about most of them will probably answer a lot of the questions that you have.0445

Now, there might be some cases where you still can't make any sense of what this thing means.0448

And in that case, just do an Internet search: type the product name of your calculator, whatever that is,0454

and then whatever the message says, into a quick search.0459

And probably, the chances are that the next thing you will have is an answer to your question.0462

You will have it figured out and fixed in no time.0466

So, just a quick Internet search will solve this for you really fast.0469

Oh, Internet, what would we do without you?0472

Oh, right, we would just look through the error messages in the manual.0474

But we have the Internet, usually, if you are watching something like this.0477

So, why do that if you can just do a quick search?0480

Of course, if you really can't figure out what it is, and the Internet is no use, try seeing if you can find a manual,0482

or email tech support for whoever makes the calculator that you are using.0486

Your graphing calculator is, without a doubt, so much more powerful than you currently realize.0491

Virtually all modern graphing calculators can do a wide variety of tasks--more than just calculations and graphing.0497

They are usually capable of working with sequences (series, as well), probability, combinatorics, matrices, statistics, finances, and many other things.0505

Normally, you have a huge array of things that your graphing calculator can do that you aren't even vaguely aware of yet.0515

So, basically, if you come across a new topic, chances are that your graphing calculator0521

already has some functionality that is connected to this new topic that you are learning about.0525

So, if you start a new topic, and you say, "Oh, it sure would be useful if there was a way a calculator could do this,"0530

just do an Internet search with the product name you have and the topic you are interested in.0535

Just search your calculator and whatever the name of the thing you are interested in is,0539

whether it is matrices or probability, and you will probably be able to find very quickly a guide for doing that specific thing with your calculator.0543

And you will be able to get an introduction to a new way that you can use your calculator.0551

The easiest way to learn how to use a new graphing calculator is just to play around.0555

I really can't encourage this enough: be curious, try new things, and see what happens.0560

Exploring on your own will do you a world of good.0565

And don't worry about somehow breaking your calculator, either; it is going to be fine.0568

Unless you have decided to explore what happens when you pound against it with a rock (hint: bad things),0572

you can't do any real harm to a graphing calculator by just playing with it.0578

In the worst-case scenario, the absolute worst possible thing that could happen is that you might change some setting0583

that causes it to work weirdly, and you can't quite get it to work in a normal way.0589

But if that happens, and you can't get it to work in a normal way, just reset the thing and put it back to factory settings.0593

You can either search up a quick way to put it back to factory settings, or most of them will have some tiny little pinhole0599

that you can press with a toothpick on the back to just put it back into factory settings.0603

And there you are: you are past this horrible, weird issue.0607

You don't really have anything to worry about; go crazy!0611

Explore; play; learn; playing around on your calculator, honestly, is probably the best way to understand how it works later on.0614

By playing around right now, you will be able to used to the stuff that you actually have to use in a year or two years' time.0622

So, it is a great thing to just play with now.0629

And that way, you will see things, so that later on, when you see new ideas and new terminology,0631

you will say, "Oh, I recognize that; dy/dx...my calculator can already do stuff with derivatives!" and things like that--pretty cool.0635

All right, in the next lesson, we will talk about actually putting a graph into a graphing calculator and some other ideas like that.0642

We will see you at Educator.com later--goodbye!0648