The onscreen keyboard allows Autograph users to input one-line mathematical expressions using a wide variety of symbols that are coorrectly interpreted, eg sin²2θ, 2x−3y≤6, −b±√(b²−4ac), y=|x| It is also invaluable when using a whiteboard or a walk-about tablet. This short video explains

It is a common request to be able to save axes settings within Autograph. The problem is where would they be stored? You would neeed a personalised preference section, not too difficult for a single user, but tricky to manage in a networked environment.

The simple answer is to save a particular Autograph page with the axes just so, then load that file when needed. This short video explains.

This video summarises the effect of a matrix transformation on different object types: the unit square, the graph of y = x², and a flag. In each case there is a variable parameter included so that animations can be set up.

Download associated Autograph file
3×3 Matrix transformations are also available on a 3D Autograph page.

This video explores the slope of a tangent on y = sin2x at x = a
and the slope of the tangent on y = sinx at x = 2a.
The Chain Rule suggests that if y = sin2x then dy/dx = 2cos2x,
so at x = a, dy/dx = 2cos2a
For the ‘parent’ function y = sinx, dy/dx = cosx,
so at x = 2a, dy/dx = cos2a, a half of the above.

In 2D: draw y = x² – 4 and y = x(3 – x).
Use Point mode, with CTRL, to locate and mark the two points of intersection.
Use the Text Box to label them (you will need the x-coordinates in the 3D page)

Double-click on ‘A’ and associate it with y = x(3 – x)
Double-click on ‘B’ and associate it with y = x² – 4
Select ‘A’ and ‘B’ (in that order), and use right-click option” Find Area”
Use Simpsons’s Rule, which gives an exact answer for quadratics (and cubics)

In 3D: draw y = x² – 4 and y = x(3 – x), using the option “plot as 2D”.
Select the top graph then the bottom graph, and right-click “Find Area”.
Enter left and right x-limits from 2D (-0.8508 and 2.351) and Simpson’s Rule
Draw x = -1 (again with ‘plot as 2D’ selected)
With ‘Slow Plot’ on, select the area and the line and ‘Find Volume’

In “Edit Axes” => “Options” you can control the grid sub-divisions as fractions of π/4. This works well normally, but if you want something special, eg grids of π/6, a good way to do this is to plot the line θ = nπ/6, and then use the constant controller ‘options’ to set up a family of lines.

Here I have drawn a family for ‘n’ = 0 to 6 in steps of 1. Note that Autograph conventionally draw’s negative ‘r’ with a dashed line, so under ‘Draw Options’ in the equation entry dialogue, set the drawing to ‘Dashed’ and then get what I have shown here.

14th February is coming up! Here is a great exercise in understanding the modulus function and the equation of a circle.

y = |x| ± √(4 – x²)

You can copy this text and paste it into Autograph (Autograph understands Unicode mathematics symbols!) First discuss what the two elements represent: y = |x| and y = ± √(4 – x²)

Later on, edit the equation (double-click on the graph) , and replace ‘4’ with ‘r²’ and set ‘r’ to be 2, so nothing is changed. Now you can now use the constant controller to set the value of ‘r’ animating from 1.8 to 2.2 in steps of 0.05 … Enjoy! (Boom-di-di-boom-di-di-boom-di-di-boom …)