Introduction to FX Draw 4

Flyout Toolbars Any tool with a red triangle hides a “flyout” toolbar containing extra

tools. Click and hold the left mouse button for > 1 second.

GAD - Geometrically Aware Drawing FX Draw provides dynamic feedback that shows the geometric

relationships in your drawing.

Make sure that GAD is turned on!

GAD Has A Memory! Any relationships that you have created with GAD are

remembered. Move the base object and all relationships are maintained.

47°

47°

Right Click Most figures have extra properties that can be accessed

by right-clicking on the figure.

Figure Information If you select a figure (anything you have drawn) and then

hover the mouse near that figure, FX Draw will display some information about that figure.

Annotations When FX Draw is displaying figure information, right click

your mouse. You are given the opportunity to add an annotation.

Annotations are dynamically updated as the figure changes.

Three Point Circles Many tools require that the object be defined by three

points – triangles, three point arcs, three point ellipses, three point circles. A good way to practice using these tools is to draw a circumcircle using the three point circle tool.

Using the Compass FX Draw 4 adds a Compass tool that works just like the

normal, centre point / point on radius tool, but then remembers the radius so the second and subsequent circles have the same radius.

Use the Compass toolto draw this “daisy”.

Marking Angles FX Draw 4 can mark angles with one-click. If you right-

click on a marked angle, you can select from 10 different angle marking options.

Angle marks are dynamic. Move the lines and the angles are re-measured.

42°

Rulers & Protractors The ruler and protractor tools let you demonstrate

measurements on paper and on screen.

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The Mathematics Tools Function Graphs Statistical Graphs Normal Distribution Curves Venn Diagrams Number Lines Grids and Dots Unit Circle Tree Diagrams Clocks

Function Graphs

Cartesian Functions Inverse Functions Polar Functions Parametric Functions Implicitly Defined Functions Systems of Inequations

Conic Sections Shaded Integrals Points and Vectors Tangent Lines Constants and Animations Complex Numbers

The function graphs tool lets you draw just about any graph that can be defined by a function

Quick Entry Screen

Cartesian Functions Enter functions in terms of x (y = is optional). FX Draw

can quickly find and annotate points of interest on the graph.

x-10 -5 5 10

y

-10

-5

5

10Point of Intersection( 2.925852 , 6.925852 )

x3 – 2x2 – 1

Local Minimum( 1.3333 , -2.1852 )

x3

23

43

53

2

y

-2-1.5

-1-0.5

0.51

1.52

Axes in terms of π

Inverse Functions Enter functions in terms of y (x = is optional).

x-10 -5 5 10

y

-10

-5

5

10

y2 + 3y – 4y

Polar Functions Enter in terms of r and th (FX Draw converts th into θ).

Inverse polar functions are supported.

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

r = 8sin 5

r = 5cos 3

= r + 2sin r

Parametric Functions Enter as x = f(t); y = f(t)

x-10 -5 5 10

y

-10

-5

5

10

x = 10sin t ; y = 10cos 3t

Implicitly Defined Functions

x-1.5 -1 -0.5 0.5 1 1.5

y

-1.5

-1

-0.5

0.5

1

1.5

(x2 + 2y2 – 2)(2x2 + y2 – 2) + 120

= 0

Systems of Inequations

x5 10 15 20

y

5

10

15

20

Conic Sections

x-10 -5 5 10

y

-10

-5

5

10

x2 – y2 + 4x – 2y – 7 = 0

(2x + 4)2 + (y – 4)2 = 40

Shaded Integrals FX Draw can shade integrals using a click & drag system

– and annotate what it has shaded!

x-10 -5 5 10

y

-10

-5

5

10

– 1.372281

4.372281

x2 – 2x – 3 – [x + 3] dx = -31.595063

Area = 31.5951

Points & Vectors Enter points as (x,y), vectors as <x,y>. You can join

points and vectors using the “+” sign.

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

Constants & Animations Placing a, b, c, d or m into an equation allows you to modify the

function dynamically. You can even put them into the bounds of integrals.

Statistical Graphs

Box & Whisker Plots Dot Frequency Diagrams Histograms Back-to-back Histograms Scattergraphs Line Graphs & MPA Bar Graphs

Column Graphs Cumulative Frequency Plots Frequency Polygons Residuals Graph Stem & Leaf Graph Triangular Graph

FX Draw 4 supports a large number of statistical graph types.

Statistics Graph Properties

Data Generators FX Draw 4 includes handy data generators that can save

you hours of time. Just fill in the blanks and push OK.

Box Plot Example Part 1 Use the Normal Random Number Generator to generate

some data into Column A – and then use the generator again to generate data with a different mean and standard deviation into Column B

Box Plot Example Part 2 Choose Quick Graph from the Right Click Menu on

Columns A and B.

Then press the Graph Type button and choose a box plot

Box Plot Example Part 3

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Other Statistical Functions FX Draw’s statistics tool can also:

Produce summary statistics for one variable and two variable data

Perform regression analysis for seven regression models Handle grouped data and frequency tables Produce frequency tables, cumulative frequency tables and

grouped data from raw data Transform data using a variety of functions

Normal Distribution Curves The normal distribution curve tool gives you quick

access to shaded normal distribution curves. You can also add annotations to the curves.

-4 -2 2 4

0.2

0.4P(-1 < z < 1) = 0.6827

-4 -2 2 4

P(z < -2) = 0.0228P(z > 1.5) = 0.0668

Venn Diagrams

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Number Lines Enter functions onto the number lines as x <= 10, x <> 4,

x = 5, x > 3. Number lines can be horizontal or vertical.

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5

Grid / Dot Papers FX Draw can produce a wide

variety of grid and dot papers.

Unit Circle The Home Key, Page Up, Page Down, Up Arrow and

Down Arrow keys can be used to animate a unit circle.

Tree Diagrams Enter a tree’s “shape” using the number of branches at

each level. For example, this tree is 4,3,2.

Gallery Images Gallery images provide hundreds of pre-drawn images

that you can use as the basis for your own diagrams.

Gallery Tips 1 Gallery images have “direction”. This means that each

gallery image can be used in many different ways. Each of these images has come from the same “base”

gallery image.

Gallery Tips 2 After you have drawn a gallery image, you can “ungroup”

it (Ungroup from the Edit menu). This gives you access to the individual components of the image and lets you modify it to suit your needs.

Email Tutorials Efofex provides comprehensive training for FX Draw 4

available as convenient email tutorials. Register at www.efofex.com/emailtutes.php. The system will send an email a day for a few weeks.

Email tutorials are available for all Efofex products.