# Basic Features & Functions of a Graphing Calculator

Instructor: Artem Cheprasov
This lesson goes over some of the basic features and functions of a graphing calculator: graphing, finding intersections, zooming, and solving equations.

## Graphing Calculators

Graphing calculators are calculators that can plot graphs and even solve equations. They make your adventures in math easier by doing some of the work for you. Isn't that great? The catch is that you have to know how to tell them what you want them to do. Graphing calculators have a ton of features, and there are many models out there. This lesson cannot cover all of them, or get close to explaining all of the functions of any one of them. But, it will give you a sense of the basic functions of a graphing calculator. We'll use the TI-89 as our base model. From there you will be able to extrapolate onto other types of graphing calculators.

## Plotting a Graph

Let's begin with the most basic and identifiable function of a graphing calculator: plotting a graph. Seems appropiate, right? You can do this using the following steps:

1. Turn on the calculator by pressing the 'on' button at the lower left hand side of the calculator.

2. Next, press the green diamond button towards the top left, then 'F1'. This will lead you to a screen that shows where you can enter the equation for your plot.

3. To keep things easy, why don't we plot y = x? Simply press the 'x' key and then the 'enter' key at the bottom right of the calculator.

4. Once you've done this, press the green diamond button again and then press 'F3'. This will lead you to your very first graph, that of y = x! You should see a diagonal line running right through the origin, where the horizontal and vertical axes intersect.

## Finding an Intersection

Now, let's do something a little bit more complicated. Go back to the screen where you entered the equation for your graph (hint: press the green diamond button and F1). Next to where it says 'y2' enter '-x' (keep the original y1 = x). Now, go back to the graph by pressing the green diamond button and then F3. You should see another line running through the intersection.

You can see that both lines run through the intersection of the horizontal and vertical axes, therefore they intersect at the point (0,0). But how can we show this on the calculator? Well, to have the calculator confirm that this is indeed where the two lines intersect, perform the following steps:

1. While on the graph screen (where all the lines are drawn), press 'F5'.

2. This will lead to a drop down menu. See where it says intersection? Press '5' to select it.

3. On the screen you'll see the calculator asking you '1st curve?'. Simply press enter.

4. On the screen you'll now see the calculator asking you '2nd curve?'. Simply press enter again.

5. Now the calculator is asking you 'Lower Bound?'. Use the arrow keys (at the top right on the calculator) to arrow down the cursor on the graph to a spot to the left of the intersection. Press enter.

6. Now the calculator is asking you 'Upper Bound?' Use the arrow keys (on the top right of the calculator) to arrow up the cursor on the graph to a spot to the right of the intersection. Press enter.

Boom! Just like that the calculator just confirmed the intersection we already suspected.

## Zooming In

Now, let's do something else. Let's find out how to zoom in and out of a graph. Perform the following steps.

1. Press the green diamond button and then F1. We see our two functions y1 = x and y2 = -x from before. Change y2 to -x + 3 to make things more interesting.

2. Go back to the graph by pressing the green diamond button and then F3.

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