FX Graph 3 Email Tutorials Powerful Graphing Made Dead Simple © 1993-2004 Efofex Software FX Graph 3 Email Tutorials User's Guide by Efofex Software Efofex Software Always check our website for our current postal, phone and fax details Email: info@efofex.com Web: www.efofex.com FX Graph 3 Email Tutorials © 1993-2004 Efofex Software All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems - without the written permission of the publisher. Products that are referred to in this document may be either trademarks and/or registered trademarks of the respective owners. The publisher and the author make no claim to these trademarks. While every precaution has been taken in the preparation of this document, the publisher and the author assume no responsibility for errors or omissions, or for damages resulting from the use of information contained in this document or from the use of programs and source code that may accompany it. In no event shall the publisher and the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused directly or indirectly by this document. FX Graph 3 Email Tutorials I Table of Contents Part I FX Graph Email Tutorial 2 1 Getting Started 2 2 Points of Interest 5 3 Points and Vectors 6 4 Annotations 1 8 5 Annotations 2 10 6 Setting the Axes 1 12 7 Setting the Axes 2 14 8 Functions Control 16 9 Moving Around the Plane 18 10 Zooming 20 11 Grids 20 12 Tangent Lines 1 22 13 Tangent Lines 2 23 14 Integrals 24 15 Function Types 25 16 Setting Domains 26 17 Constants, Animations and Families of Curves 29 18 Inequations 31 19 Feasible Regions 33 Index 0 © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1 FX Graph Email Tutorial 1.1 Getting Started FX Graph Email Tutorial 2 Load FX Graph from the Start menu - you will see a blank set of axes. Lets draw a simple quadratic graph. Push the button to enter a function. Alternatively you can move the mouse to a blank part of the FX Graph window and right-click. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 3 I have typed x2-4x+1 into the top line of the functions. Notice how a formatted version of this is shown. Press OK and our graph will appear. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 4 The function entry section of the Quick Entry screen allows for multiple lines. Each line will be graphed as a separate function. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1.2 FX Graph Email Tutorial 5 Points of Interest Points of interest include things like: Intercepts Turning Points Points of Inflection Points of Intersection FX Graph finds points of interest automatically. As you move the mouse around, FX Graph will show you any points of interest near the cursor. There are two important things to note: 1. FX Graph will only show the point of interest if you "hover" near it. In other words, the message will only be shown if you leave the mouse still for a short time. 2. Points of interest are calculated NUMERICALLY rather than algebraically. This sometimes results in slight errors. Notice how the point of interest message is colour coded to the function curve. Points of intersection are coloured yellow. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1.3 FX Graph Email Tutorial 6 Points and Vectors FX Graph allows you to draw points and vectors on the plane. Points are entered in the Quick Entry screen in exactly the same way as a function (see above). You can separate the points with semicolons but this is not strictly necessary. Vectors are entered as <2,4> If you enter the following: (1,0)+(1,5)+(3,4)+(1,3) you will get the following © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 7 The + signs force FX Graph to "join the dots". By adding + and - signs to a list of vectors, you can get FX Graph to show vector additions and subtractions. <1,3>+<5,-8>-<3,1> © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 8 You can also combine points and vectors together. Try entering this... (-2,3)+<1,3>+<5,-8>-<3,1> FX Graph can also handle Polar points and vectors. We will discuss this in a later lesson. 1.4 Annotations 1 FX Graph provides lots of transient information as you move around the graph. If you want to keep information on the graph, you need to add an annotation. FX Graph makes adding annotations easy. First, you need to enter Annotation mode. To do this, push the toolbar. button on the You can now add annotations in one of three ways. 1. Left Click on a blank area of the graph. FX Graph will add a blank annotation that you can edit later. The annotation will display the words "Right Click to Edit". 2. Left Click and hold the mouse button down. Move the mouse in the direction © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 9 of the arrow you want and then release. The annotation will again display the words "Right Click to Edit" but it will also have an arrow attached to the annotation. These two types of annotation are show below: The second annotation has an "anchor" that the arrow is pointing to. 3. The final way of using FX Graph's annotations is by far the most powerful and useful. Move your mouse until FX Graph displays a message (a point of intersection for example). Left click the mouse while the message is being displayed and FX Graph will create an annotation that contains the same message and is anchored to the point of interest. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 10 Once you have created your annotation, you can move it around with the mouse. You can also move the anchor point around if it is not attached to a point of interest. You can delete annotations by selecting them and pushing delete. We will discuss editing annotations in the next lesson. 1.5 Annotations 2 Editing annotations is easy - just right click on them. When you do, you will see the following dialog box. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 11 Each of the ten available lines has a check box next to it. In the above example, the first line is checked and the second line is not. This check box tells FX Graph whether to treat the text as an equation or not. In our example, FX Graph would treat the first line as an equation and will display it as: FX Graph has turned the text into a formatted equation using Efofex's equation technology. There is a email tutorial series discussing how to use this technology if you have not seen it before. Using the Edit Annotation screen, you can also edit the font used and the type of anchor used. There are two important buttons on the Edit Annotation screen that we would like to point out - the Set as Default button and the More >> button. The More >> button will expand the dialog box and display more options. These are the less used options that would just be confusing if always shown. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 12 Many of our screens have a More >> button. The Set as Default button will take your current settings for annotations and make them your standard. This lets you set things up exactly as you want them and then keep them that way. Most of our screens have a Set As Default button. 1.6 Setting the Axes 1 Setting Axes is often one of the most tedious parts of using a graphing program. FX Graph makes it just about as simple as it can be. First up, we will discuss how to set the axes using the Quick Entry Screen. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 13 Setting the axes in the Quick Entry screen gives you quick results with a little less control. It is a two stage process. 1. Move the sliders marked above to get the shape you are after. You might wish to graph a trigonometric graph for example so you would set the sliders as 2. Set the maxima for the x and y axis. Because we are graphing a trigonometric function, I will set the y maximum as 1 and the x maximum as 2pi © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 14 The 2pi tells FX Graph to mark the x axis in multiples of pi. That is all there is to it. Push the OK button Most of the time, you will be able to get a perfectly adequate set of axes using this method. If you need more control, it is available to you and we will discuss this in the next lesson. 1.7 Setting the Axes 2 To gain more control over the axes, you need to use the Axes Properties dialog box. You can get to this by: Right clicking on the axes or Pushing the Axes button in the Quick Entry Screen. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 15 The Axes Properties dialog box has a More >> button. The image below shows you the smaller version of the dialog box. Here we can set the minimum and maximum values for both axes. You can also override the automatically generated ticks. Ticks are the scale marks on the axes. Major ticks have numbers on them. Minor ticks don't. If you wish to override the automatic ticks, you need to uncheck the check boxes next to each setting so FX Graph knows that you are taking responsibility for the settings. The final setting in the Axes Properties box is Scales. This gives you control over how FX Graph sets up the axes. "Free" - means that FX Graph will fill its available space using your maxima and minima © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 16 "Equal Aspect" will ensure that distance per unit on the x and y axis are the same. This will often cause your graph to not fill the rectangle. You need to use Equal Aspect to make many mathematical relationships look correct - especially polar graphs. It is also important when you look at gradients. "Fixed" sets the scale to a particular measurement. You set exactly how many millimetres constitute one unit on the x and y axis. When you do this, FX Graph ignores your maximum and minimum values because the graph's extent will depend on how much room you give it. NOTE: If you resize a graphic FX Graph has generated inside another program (like Word), this "fixed" size will no longer hold true. Finally, there are quite a lot of options that determine how the axes are displayed to suit different school systems around the world. Many of them are available by going to the Tools menu and choosing Preferences. You should consult the manual to understand all of the available settings. 1.8 Functions Control The Quick Entry screen lets you create functions quickly but many aspects of functions cannot be adjusted in the Quick Entry area. You can quickly adjust functions by right-clicking on them. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 17 This right-click menu allows you to show or hide domain marks, vertical asymptotes and arrowheads. You can also turn on the 1st and 2nd derivative curves. If you choose Edit Properties, the Function Properties screen will appear. This screen gives you full control over the function. Notice that we are looking at Function Number 1, the first function entered in the Quick Entry screen. You can cycle through all entered functions on this screen. If you load this screen by right-clicking on the function, you will automatically be taken to the correct function number. You can also load the Function Properties screen by clicking on the Functions button on the Quick Entry screen. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1.9 FX Graph Email Tutorial 18 Moving Around the Plane If you have a graph such as the one below you might suspect that there is something interesting happening higher up the y axis. How do you get up there to see it? You could go into the Axes Properties and adjust the axes or you can use the arrow keys to move around the plane. We want to move up the y axis, so press the up arrow a few times. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 19 The graphs look about ready to intersect - so lets go further. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 20 We can now see the point of intersection (marked). Notice that FX Graph has "broken" the y axis. FX Graph is quite happy to break the axis but you can turn off the behaviour if you wish. You can move all over the plane using the arrow keys. If you wish to return to the origin, just push the Home key. 1.10 Zooming FX Graph's automatic detection of points of interest largely eliminates the need for zooming in on different parts of the screen but FX Graph can zoom if you need it. There are three ways of zooming in. Keyboard. In the last lesson we moved around the plane using the arrow and Home keys. You can Zoom by using the Page Up and Page Down keys. Page Up zooms out and Page Down zooms in. You can also zoom using the mouse but you first need to change to Zoom mode. You do this by pushing the button on the toolbar. One Click Zooming. When you are in Zoom mode, you can zoom in by left clicking on the graph. FX Graph will zoom in, centred on your click. Rectangle Zooming. When you are in Zoom mode, you can use your mouse to sweep out a rectangle on the graph. FX Graph will zoom in to the rectangle you mark. As you Zoom In, FX Graph remembers the axes at each step. You can backtrack by Right-clicking your mouse. 1.11 Grids FX Graph 3 can draw a wide variety of grids. Open the Quick Entry screen and press the Grid button - what you see next depends on whether you are showing the grid as lines or points. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 21 Most of these settings are obvious but there is one vitally important point that is sometimes forgotten. No matter what settings you choose in the Grid Properties dialog box, nothing will appear on screen until you tick the Show Grid box in the Quick Entry Screen. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1.12 FX Graph Email Tutorial 22 Tangent Lines 1 You can add a tangent line to any CARTESIAN function. This can be done in one of two ways: Using the Menus Choose Tangent Line from the Tools menu (the option will be greyed out if there are no suitable functions). The Tangent Line dialog box will appear. Select the function you wish to attach the tangent line to and the point at which to start and FX Graph will attach it. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 23 Using the Mouse First, push the button and then simply click on the desired location. FX Graph will attach a tangent line at the location. 1.13 Tangent Lines 2 Selecting a Tangent Line You can select a tangent line by choosing Select mode by pushing the and then clicking on the tangent line. button Moving a Tangent Line Once a tangent line is selected, you can move it on the function by pushing the left and right arrows Editing a Tangent Line Right click on the tangent line to edit its properties © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 24 Adding Multiple Tangent Lines Normally, FX Graph restricts you to ONE tangent line per function - but you can add more. Try adding a tangent line (using the mouse) to a function and then try to add a second one. FX Graph will just beep. If you really want a second tangent line on the SAME function, hold down the Ctrl key when you click. 1.14 Integrals There are two ways of creating Integrals in FX Graph 3, using the menus and using the mouse. First, create two simple Cartesian graphs. Using the Menus Go to the Tools menu and choose Integral. The Calculate Integral dialog box will appear. Here you can create an integral to display. Notice that in FX Graph 3 you can find the area from the curve to the y Axis. Push OK and your integral will be created. Using the Mouse Select the Integral mode by pushing the button. Move the mouse so that it hovers over the function you wish to find the integral under. FX Graph will automatically lock onto interesting points such as intercepts. Click and hold the left mouse button. Move to the other end of the integral. Release the mouse button. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 25 Your integral will be created automatically. If your starting point is one a function, FX Graph will calculate and show the integral under that function. If your starting point is the intersection of two functions, FX Graph will calculate and show the integral between the two functions. Editing an Integral Right click on any integral to change its properties. Adding Multiple Integrals Normally, FX Graph will restrict you to one integral on a set of axes. If you create a second integral, the first one will be replaced. You can create multiple integrals by holding down the Ctrl key as you create them with the mouse. 1.15 Function Types FX Graph can graph many types of functions. It works out what you want by how you enter the function. For example: © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 26 x2+2x-7 Cartesian function. FX Graph assumes you mean y = x2+2x-7 y3-3y Inverse Cartesian function. FX Graph assumes you mean x = y3-3y x+y = 4 FX Graph will rearrange it automatically to graph x2-3y2=5 FX Graph will detect the conic and draw both sides r=3th FX Graph uses th for theta. It will draw a polar graph th = r2+4 FX Graph will draw an inverse polar graph x=3sin t; y = 3cos 2t Placing two equations, in terms of t, separated by a semicolon, will let FX Graph draw a parametric function 3sinx/2+4cosy/2x=xy FX Graph can graph complex implicitly defined functions such as this but it performs much less analysis on the results (2,3) (3,4) (4,7) FX Graph will plot three points (2,3)+(3,4)+(4,7) FX Graph will plot the same three points but will "join the dots" as it goes <2,3> FX Graph will plot a vector from the origin to (2,3) (2,3)+<1,1> FX Graph will draw a <1,1> vector starting from (2,3) (1,1)+<1,3>+<3,4><1,2> FX Graph will show the indicated vector additions and subtraction starting from (1,1) P(1,pi/2)+<1,pi> Placing a P before a point/vector combination will tell FX Graph to treat the points and vectors as polar points and vectors. Try it out! 1.16 Setting Domains There are a few ways of setting domains in FX Graph 3. The Old FX Graph 2 Way Push the Functions button on the Quick Entry screen © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 27 Here we have typed a domain for x2. We could have also entered a domain such as x > 2 or x < -3. On the Same Line as the Function Alternatively, you can now just type the domain AFTER the function in the Quick Entry screen. All you have to do is to place a separator (semicolon in most countries) after the function. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 28 Using (-2,3] Notation Finally you can now express domains using bracket notation. You can do this either on the same line as the function or on the Function Property screen. When you use bracket notation, you do NOT need to use a semicolon. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 29 Domains are particularly important for polar and parametric functions. Finally, you can use constants and pi in the domain. A domain such as (a,pi] is perfectly acceptable. 1.17 Constants, Animations and Families of Curves FX Graph can accept up to five constants in any equation. The five constants are a, b, c, d and m. To use constants, just enter them as part of the equation or domain. FX Graph will find them and will display "constant controllers" for each constant you have used. For example, if we enter the function ax2 + bx + c FX Graph will show © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 30 You can now control each constant individually. The buttons at the bottom of each controller let you generate families of curves and animations. Family of Curves If you push this button for the 'a' controller, you will be able to select start, stop and increment values for a. These settings will produce this family of curves. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 31 Animations You can animate a constant by pushing this button. Importantly, you can change the other constants while you are animating. Try it. 1.18 Inequations FX Graph can graph most Inequations. y >= x+2 x + y <= 4 x2+y2 > 25 © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 32 Your display could look quite different to this as FX Graph has four ways of shading feasible regions. We will discuss shading in the next lesson. FX Graph can shade inequations for most functions including polar functions. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials 1.19 FX Graph Email Tutorial 33 Feasible Regions FX Graph can shade the feasible regions resulting from inequations in one of two main ways. You can control how FX Graph shades feasible regions by opening the Quick Entry screen and pushing the More >> button. The main Feasible Region Shading options will appear. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 34 Half Planes This option shades the total area that agrees (or disagrees) with each inequation. The above functions will produce one of these two graphs. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 35 © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 36 In the left hand graph, FX Graph has shaded the half planes that agree with the inequations, on the right, FX Graph has shaded the sides which disagree. Some school systems prefer the left hand style, some the right hand style. You can choose which style to use by going to the Tools menu and choosing Preferences. ONLY Feasible Region With this option set, FX Graph calculates the area that satisfies all the inequations and shades only that region. © 1993-2004 Efofex Software FX Graph 3 Email Tutorials FX Graph Email Tutorial 37 FX Graph will try to shade the region using solid shading if it can. If the relationships are too complex, it will shade the feasible region using an array of dots as seen in the last lesson. © 1993-2004 Efofex Software

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