Saturday, February 4, 2012

Graphing Calculator Part 1: Graphing

Mathematics is cool in itself with the proofs and patterns, but there are also tools in mathematics that are pretty cool as well. One of which is the graphing calculator. For the majority of February, I will be teaching how to use a TI-83 graphing calculator, and you will be able to use it and appreciate it as much as your iPods and iPhones.

First of all, these things only work on TI-83s and mostly on TI-84s as far as I know. I'm not sure about other types of calculators, so don't get confused with a different type. If you have either of those, take it out now so you can follow along. If you don't, you are missing out on some awesome mathematical technology, but you should be able to get the vive of what a graphing calculator is.

Okay, now to the fun stuff. What does a graphing calculator imply it should be able to do? Graphing, right! And it's as easy as ever with these devices. Let's say you want to graph 3x - 7.

First, we will turn on our calculators (in the bottom left corner). Now, two from the left on the very top is a purple button with the word window on it. Click that.

This screen enables us to choose what we want our graph intervals to be. First, we will choose what we want our X-minimum to be, called Xmin on the calculator. Let's put in -10. The negative button is one to the left of the Enter button, in white. Don't use the blue minus button, that won't work on the calculator.

Now, we have to choose an X-maximum. To keep things consistent, we'll use ten. Use the enter key as if it were a return key.

Next, we must look at the X-scale, labeled as Xscl. This basically makes a little mark at every interval you type in. I am going to put in five, just so there aren't too many of them on the graph. However, if you want to see intervals of two, feel free to put in two. Make sure you don't put a negative there!

For the y-values, we can change them up, but I will do the same as we did for the x-values. -10 for Ymin, 10 for Ymax, and 5 for Yscl. Leave Xres alone as one.

If you click the purple "graph" button now, you will see your Cartesian plane, with little marks at (-5, 0), (0, 5), (5, 0), and (0, -5). These are simply the intervals, which were correctly placed. If you see then at all of the even intervals, then you put 2 in for Xscl and Yscl.

Now, we will graph the line. To do it, click on the purple "Y=" button, which is right to the left of the Window button. It should come up with Y1, Y2, and so on. The curser should be next to Y1, where we will type in the equation. Type in a 3, then X. X will appear if you press the X,T,Θ,n button, which is a black button located one to the right of the green Alpha button. Now, press minus (not negative this time), and then seven. Now, hit graph again.

The calculator should have graphed the line right before your eyes. Pretty cool, huh!

Say you wanted to know what y was when x = 2. There's no need to approximate with your line. Simply  do the following:

1. Hit the calc button. To do it, click 2nd, then Trace. This will bring it up for you.
2. Click on the first choice of value. To do that, simply hit enter.
3. The graph should be brought up again with X= in the bottom corner. Type 2 into the calculator (since two is the value we want), then hit enter.
4. The calculator should have come up with Y=-1 in small print to the right of the y-axis. It has also put a little x over the point (2, -1) to show you where it's located on the graph.

The cool thing is that now that you have set up your window, you can graph anything you want. Say you want to graph -0.5x^2 + 5x - 5. Just click Y= and punch it in, and it will come up with the graph. To do the power, you can do one of the following:

1. Click the carrot just above the division sign, and then a 2
2. Hit the x^2 button to the left of the comma

Say you are curious as to what a quartic equation looks like; an equation with degree four, or an x^4 term in it. Try graphing x^4 - 5x^3 + 4x^2 + 6x - 8. It's pretty cool.

You can also look at trigonometric graphs. Try graphing the tangent of x, or tan(x). It's pretty cool!

Here's something I want you to try to graph:

Y1 = sin(x)
Y2 = sin(x+2)
Y3 = sin(x+4)

Those three look really cool together!

Tip: Remember not to use a minus sign for a negative. It will always mess up something that you were working on for a long time.

If you don't own a graphing calculator, but want to check out these graphs, I'd recommend The picture of the graph is better, but it doesn't have the same freedoms as a graphing calculator, as you will see next week.