Like it or not, learning how to use a graphing calculator is a vital part of your education. Even if you know for a fact that math is not an essential aspect of your future career, learning a wide variety of subjects will help develop you into a critical thinker.
You may be surprised by how many fields of study rely on mathematics for their framework. For example, what would sociology be without statistics? It would probably just be philosophy.
Even creative skills, such as art effectively utilize graphs. In any case, knowing how to use a graphing calculator actually makes math easier.
NOT YOUR AVERAGE CALCULATOR
Graphing calculators seem intimidating at a glance but are quite simple in reality. It will just take you a little time to get used to the interface.
You're probably familiar with a standard calculator; the kind that comes with numbers zero to nine, and buttons for basic addition, subtraction, multiplication, and division. There are a few other options, but that's about it for an ordinary calculator.
In contrast, a graphing calculator contains extra buttons for accessing menus and using various functions. Many of the buttons do two or even three things. If this were not the case, then your calculator would be enormous.
All graphing calculators possess the ability to store information for later use, allowing for more complicated processes. Other calculators don't have this.
If you typed 27 * 39 on a standard calculator and hit equals, it would give you the answer 972. But if you then started entering a different number, it would completely forget that 972 existed.
Of course, the most significant feature of a graphing calculator is the ability to create graphs. Once you know where and how to enter the information, your calculator can take functions or data points and turn them into visuals. These can be line graphs, bar graphs, scatter plots, and more.
WHY A GRAPHING CALCULATOR?
You may be wondering, "why do I need to know how to use a graphing calculator when I can do all of this in excel or other programs?"
Well first of all, if you're that proficient with spreadsheets then hats off to you. However, graphing calculators are generally better for quick personal reference as they take less setting up. In any case, spreadsheets won't be an option on your SATs or other exams.
When it comes to completing functions and equations without graphing, you may be able to get by with an ordinary calculator. But knowing how to use a graphing calculator will make you much faster because you can just enter the information and let it do the work for you.
That's not to say that going through all the steps on your own isn't good practice. For the sake of saving your precious time, though, why make it harder on yourself?
HOW TO USE A GRAPHING CALCULATOR: THE BASICS
Now that we've established that they do indeed have a purpose grab your TI-83, TI-84 or another graphing calculator, and get ready to learn.
The first step is, of course, to turn it on. To do this, simply hit the ON button in the bottom-left corner. Notice that OFF is written above the button in orange or blue text. In order to turn the calculator off, press the orange or blue 2ND button near the top-left and then press ON.
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It's possible that you will attempt to turn the calculator on and nothing will happen. Before changing the batteries, try increasing the brightness.
To do this, hold the 2ND key and simultaneously press the up arrow towards the right side calculator. If you'd like to decrease the brightness, press the down arrow instead.
Getting to know your calculator
As you learn how to use a graphing calculator, you'll find that there are certain buttons you utilize often, and others that you rarely use if ever.
It's unlikely that you'll need these without someone explaining to you how to use them, so don't worry about it. We'll be going over the most commonly exploited features in detail.
Frequently used buttons
You already recognize some of the buttons from your standard calculator. However, you'll notice that CLEAR replaces the C and CE buttons for erasing things. It will delete everything, while the DEL key will backspace.
The topmost buttons along the bottom of the screen are used to access menus. Use the arrow keys to navigate menus and equations.
To access the orange (or blue) and green features of a button, use the 2ND and ALPHA keys respectively. For example, press 2ND and then MODE to QUIT out of whatever menu you're in.
Using ALPHA allows you to access every letter in the alphabet by pressing it and then pressing the button where the letter is in green.
Contrary to popular belief, these letters are not for passing notes in class! They are for variables in equations, which we'll get to later.
More buttons
If you want to square a number, first put it into the calculator, then press the X2 button and hit enter. You can do the same to find the square root key, but press 2ND before hitting X2.
The ^ key can also be used to square a number, or for any exponent. For example, find 17 to the power of 3 by entering 17^3 and pressing ENTER.
If you're taking trigonometry, you'll be using SIN, COS, and TAN a lot. The inverse of those functions can be accessed by first pressing 2ND. So, providing a decimal and hitting 2ND and then SIN would give you sin-1, which is one way to find an angle on a triangle.
The last button we'll discuss here is the (-). Use this to make a number negative by pressing it before entering the number.
There are, of course, many more features besides these, but this should give you a general idea of how to use a graphing calculator.
Order of operations
Consider the equation 3(4-12^3) + 7^4 - 3(5). With no understanding of the order of operations, you might try to solve it from left to right. Even then you'd probably have a hard time coming up with an answer.
Chances are you've heard of PEMDAS, and you know that you should resolve the exponent first. On a standard calculator, you'd have to sit there and type out 12 * 12 * 12, get the answer 1724, erase it, and type 4 - 1724.
Congratulations, you solved one small part of this equation!
Luckily, on a graphing calculator, it's much more manageable. Simply type out the equation as you see it and the calculator knows how to solve it. Not only is this less of a headache, but you're not as likely to make mistakes.
The store key
Sometimes you'll have an equation that uses one or more variables, and you'll want to assign a number to them before solving an equation. What if the equation we talked about was actually X(4-12^X) + 7^4 -X(5) where X is equal to 3?
You could just replace every X with 3, but for the sake of consistency, there is another way. First, enter 3 and hit STO->, which stands for store. Then type X by pressing ALPHA then STO-> because that's where you write X in green.
Next, you press ENTER. The number 3 is now stored under the variable X, so anytime you type X in an equation it will act as if you typed 3.
HOW TO USE A GRAPHING CALCULATOR: GRAPHING FUNCTIONS
You've come a long way in understanding how to use a graphing calculator. Next, we're going to discuss how to create actual graphs.
There are two ways to make a graph. The first is by using a function, such as Y = 2X + 3.
When creating a graph in this way, the calculator will automatically create the points for when X is equal to 1, 2, 3, and so on. This is useful for very complicated equations where you can't easily solve for Y in your head.
To begin, press the Y= button on the top-left. A menu will open with a list that looks like Y1=, Y2=, Y3=, etc. Scroll through the list using the up and down arrow keys. Notice the blinking box next to the Y you have selected.
With Y1 selected, type 2X + 3. Now hit the top right button that says GRAPH. Voila! You have yourself a graph! Use the arrow keys to select different points on your graph to see what they are.
Multiple functions
Usually, you'll only need Y1, but sometimes you may want to have multiple functions graphed simultaneously or simply have more than one function stored.
Press the Y= button again, scroll down to Y2 and enter X^2 + 3. Hit GRAPH to return to your graph. You now have two functions graphed, the second of which is a parabola.
You can turn a function off without deleting it, so it is ready to be activated later. Go back to your functions with the Y= button and scroll to Y2. Then tap the left arrow key once so that the equals sign is selected and press ENTER.
Tap the right arrow key. The equals sign no longer has a box around it like the others because it is deactivated. If you press GRAPH, you will see that only the Y1 function is displayed.
You can turn the Y2 function back on in the same way you turned it off.
Tables
Graphs are great for getting a sense of how a function behaves. For example, without looking at any of the numbers, it's easy to observe that our Y1 function has a steady positive slope. In contrast, our Y2 function has Y increasing exponentially with every increment in X.
But when it comes to the actual numbers, tables can be much easier to read because they tell you in a list format that when X equals 3, Y equals 12.
To access a table of your functions, just press 2ND before hitting GRAPH. It's as easy as that. You can turn functions on and off the same way you do for the graphs, and only the activated functions will be displayed.
Use the up and down arrow keys to scroll through your list. You can go as high or as low as you want to. Want to know what Y equals when X is -2782? Go for it.
HOW TO USE A GRAPHING CALCULATOR: PLOTTING DATAPOINTS
The other way to create graphs is by plotting data points. Use this when X does not directly influence the value of Y. For example, let's say our first point is 2, 7. So X is 2, and Y is 7.
Our second point is 3, 20. There appears to be no relationship between the two points, and so using a function to express them is impossible. Instead, we will create a plot. You'll use these a lot in statistics.
First, make sure that the functions we previously entered are deleted or deactivated. We don't want them interfering with our plot.
Next, press the STAT button located near ALPHA. This will take you to a list of options. The only one we care about at the moment is Edit. With that selected, hit ENTER.
Entering lists
You now have three lists; L1, L2, and L3. L1 is going to represent our X values, while L2 will be our Y values. You might recognize that we are essentially creating a custom table.
Enter in about five values each under L1 and L2. Use the arrow keys to move around the lists. When you've finished, press 2ND then Y= to go to the Stat Plot screen.
Select On and hit ENTER to turn on the stat plot. You can also change the type of plot from this menu from a scatter plot to something else like a bar graph.
Finally, locate the ZOOM button near Y= and press it. Scroll down to where it says Zoom Stat and press ENTER. Whew! Your plot is now ready to go.
Stat plots are extremely useful for statistics, because although Y might not be a perfect product of X, there may be a positive or negative correlation between the two. For example, when X increases, Y may tend to decrease.
READY FOR ADVANCED FEATURES?
You are well on your way to understanding everything about how to use a graphing calculator. Although it might only seem like the tip of the iceberg, you've conquered the most significant hurdles.
Now when you come across something new, you'll be able to quickly look it up, or even figure it out for yourself.
Do you have question, concerns, or suggestions about other ways to use graphing calculators? We invite you to post your thoughts in the comments below.
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