## Tuesday, March 20, 2012

### Calculator Help: Input Functions

This post is the first in a series I’m doing that will help you use your graphing calculator. The calculator I’m using for demonstration is a TI-84 Plus Silver Edition graphing calculator. These instructions apply to any TI-83 or TI-84 calculator. If you are using an older model, such as a TI-82, the steps are essentially the same, but some buttons/menus will be in different places. If you are using a newer/higher model, such as the TI-89, most of the buttons/menus will be in the same place, but your screen may look different than mine.
Also, I have the newest operating system on my calculator. The new operating system differs from the old in that it handles fractions more easily. If you are interested in downloading the new OS to your calculator, you need to have the TI Connect software and a mini-USB to USB cable. Your calculator, if bought new, should have a CD with it and a cable. If you don’t have the CD, the software can be downloaded from the web and you can use any mini-USB to USB cable you may have around.
It is not necessary to have the newest OS on your calculator for my demonstration purposes. I just wanted to explain why my calculator screen may look a bit different than yours.
Today’s lesson will cover how to graph functions. We will input functions into the calculator and adjust the window settings to see the function in the GRAPH screen.
For this explanation, we will be using the Y= menu, the WINDOW menu, and the GRAPH screen. You can get to these menus and screens via the buttons circled in yellow (Y=), red (WINDOW), and green (GRAPH). We will also use the ZOOM key, which is to the right of the WINDOW key (not circled) and the variable key, which is to the right of the ALPHA key (circled in a later photo).
Take a minute to go through these menus and get familiar with them.
When inputting a function into the calculator, you need to solve for y first. That is, the calculator only understands functions if they begin with “y=.” Your function may use other names for y, such as f(x), g(x) or something similar. Simply replace this f(x) or g(x) or whatever with y. Also, your function may use some other variable than x, so you can simply replace that variable with x because the calculator only recognizes the variable x in a normal function.
Before going over the steps to input a function into your calculator, there are two things you need to check first. Open the Y= menu and check these two things:
1.  Is there a function (or more) in any of the Y slots? If there is, arrow to that slot and press the CLEAR button to erase it.
2.  Is one of the Plots at the top of the screen highlighted? If one is (or more are) highlighted, arrow up and over to it and press ENTER to disable it. (To check this on the TI-82, you will have to press 2nd, then Y=, and then choose option 4: PlotsOff, then ENTER on the home screen to turn all stat plots off.)
How to Input a Function
1.  Solve the equation for y if it is not already in the correct form.
2.  Open the Y= menu and type the equation into the first entry, beginning after the equals sign. Fractions must be input between parentheses. The variable x is entered using the variable key (circled in red on the calculator image below.)
3.  Press GRAPH to graph the function. If you cannot see this function in your screen, press ZOOM, and then choose option 6: ZStandard to return your window to the standard window dimensions. We will discuss how to alter the window for other functions later.
The term window refers to the viewable area of the graph screen. The standard window is x: (-10, 10) and y: (-10, 10), both with scale set to 1. This means that in the standard window, you can see from -10 to 10 on the x-axis and from -10 to 10 on the y-axis and there is a tick mark for every 1 unit. For many functions, this graphing window is acceptable and all important aspects of the graph will be shown. For others, however, this window may not show some important characteristics of the graph, and you will have to manually adjust the window.
Graph the following function using the steps above.
You should see the image below in your GRAPH screen.
Notice that the function is quadratic with a y-intercept at -32. The standard window, however, is not large enough to show this y-intercept. Therefore, we must adjust it. Use this graph to follow the steps below and adjust the window to see the y-intercept.
How to Adjust the Graphing Window
1.  Graph the function.
2. If you already know which pieces of the graph are not showing, you can skip this step. If you are not sure which part of the window needs to be altered, press ZOOM and then choose option 0: ZoomFit. This should allow you to see the important parts of the graph that were previously hidden. However, you should still adjust the window further to allow for a clearer picture.
3. We know that the function we’ve graphed has a y-intercept at -32, so our minimum y-value shown must be at least -32 for us to see the whole graph. Press WINDOW and arrow down to Ymin and input -50 here. Our window is now x: (-10, 10), y: (-50, 10), and both scales are 1. With our y range so large, however, the axis will be very cluttered with a y scale of 1. So let’s change Yscl to 10 so that there will be a tick mark every 10 units on the y-axis.
4. Press GRAPH again to view the changes we made. The graph is now clearer, easier to read, and the important minimum value is easy to see.
You may need to adjust the window a little at a time until you are satisfied with the graph you see. It may be helpful to manually find the y-intercept first, so that you can get an idea of where the function crosses the y-axis. You can also manually find the x-intercepts for the same reason.
Adjusting the window is not a set process because it works differently for every function. You will need to play with it by making small changes and returning to the graph to view them.
I hope this post has helped you feel more comfortable with inputting functions into a calculator for graphing.