FX Graph 3 Email Tutorials

FX Graph 3 Email Tutorials
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
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FX Graph 3 Email Tutorials
© 1993-2004 Efofex Software
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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
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FX Graph 3 Email Tutorials
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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.
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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.
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The function entry section of the Quick Entry screen allows for multiple lines.
Each line will be graphed as a separate function.
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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.
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FX Graph 3 Email Tutorials
1.3
FX Graph Email Tutorial
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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
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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>
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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
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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.
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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.
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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.
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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.
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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
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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.
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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
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"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.
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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.
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1.9
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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.
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The graphs look about ready to intersect - so lets go further.
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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.
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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.
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1.12
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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.
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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
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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.
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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:
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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
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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.
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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.
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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
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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.
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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
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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.
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1.19
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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.
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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.
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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.
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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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