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Graphing Calculator: Functions Modes
The function mode setting allows you to graph functions, parametric functions, polar functions, and sequences. The key will automatically use the correct variable depending on the setting you choose. When you use the key in function mode, an X will appear. In parametric mode, T appears. Polar mode will display q and n will be displayed in sequence mode. The y= screen will appear differently depending on the setting you use. Let’s begin by looking at functions.

In function mode, I want to graph y = 2x2 - 3x + 1. When I press the button, I see the following screen.



To enter the x variables of my function, I simply use the key. The graph is shown below.



For most graphs you need to create, function mode is the one you need. However, the other modes are also very useful and interesting.


Parametric equations are defined in terms of a parameter, the variable t, and require an x and a y equation. This is indicated when you change to parametric mode and press the key.



You cannot enter only an x or only a y equation. Both are necessary for graphing. Let’s graph the following parametric equations.



The window settings are a little different in parametric mode too. Instead of simply having to set minimum and maximum values for x and y, you must also do the same for t.

The values of t act as a counter. So if you only want to use values of t from 1 to 5, those values should be your Tmin and Tmax. The Tstep determines how many times the calculator plugs t into the x and y equations between 1 and 5. So if you only want 5 values, set the Tstep at 1. If you want more, set it at 0.5 or 0.1 or any other increment you choose.



This graph represents x and y values that are calculated using t values form 1 to 5.



Modeling vertical and horizontal motion can be done in parametric mode. It is a little more complicated than the example done here and the end result graph is not very interesting, but it does provide a nice visual aid for motion problems. For more information, click here.

Polar mode allows you to graph polar function defined in terms of an angle q. The key now produces when used. The Y= screen is



You can graph polar functions like r = 2 sin(2q). Polar function usually appear in precalculus and trigonometry.

Again, the window key will not just have settings for x and y. You must now set values for q. A good initial setting is from 0 to 2p with a scale of p/20. You can enter these values using your p key, but as soon as you press ENTER, the calculator will change the values to a decimal approximation. Be careful that if you are entering radian measures in your window screen that the calculator mode is set in radians. If you need help doing this, click here to go the Calculator Mode lesson.

The other settings are from -2 to 2 with a scale of 1.



Using these settings, the graph looks like this.



Polar graphs are usually nice pictures that are tedious to graph by hand but quick and easy on the calculator as long as you set everything up correctly.


Finally, sequence mode allows you to graph arithmetic, geometric, or recursive sequences. The key now gives you n which is the variable in sequence mode. The key gives you



You set nMin where you would like the start to count. The sequence is defined in the u(n) setting and u(nMin) is the value of the sequence at your starting point.

Suppose you have the arithmetic sequence: 3, 7, 11, 15, 19, . . . where you are adding 4 to each of the previous terms.

For this sequence, your settings in the Y= screen are:



The u(n) is indicating that you are adding four to the previous term. The nMin=1 and u(nMin)=3 work in conjunction to tell you that the first term (nMin=1) is equal to 3.

The u(n) and u(nMin) must be used together. Sequence mode does not work if only one or the other is entered.

Before obtaining a graph of this sequence, you must set the window. As with parametric and polar modes, the window screen has settings for variables other than x and y.



The nMin and nMax settings tell the calculator how many terms of the sequence you want. The x values should correspond to the n values you use. The y values should correspond to the numbers in your sequence. The graph of our sequence is:



When graphing in sequence mode, even if your calculator is set in connected mode, you will only see points. That’s because a sequence is a listing of numbers without other values between them. If you express this sequence as the function and graph it in function mode, you will be able to see a line rather than a set of points.


As you can see, by changing the function mode setting, the calculator adapts its variable input key, its Y= screen, and window screen settings to accompany the mode. For lessons that make further use of these modes, click below.

links to motion problems in parametric mode, polar graphing, and sequence lesson.



S Taylor

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