The Graph Button (used with multiple equations in the listbox)
If the List Box contains multiple equations separated by commas then clicking on the
Graph button will cause the Algebra Coach to draw multiple curves on the same graph.
You can then adjust various graph settings and when you are satisfied with
your graph you can click the Copy to Workspace button
to make a copy of it on the workspace. Then you can close the Graph window.
You can draw three types of graphs:
- y versus x graphs. Each equation produces
one curve on the graph. The equations may be expressed in either
explicit form (for example the straight line y = 2x + 3) or implicit form
(for example the circle x^2 + y^2 = 9).
No variables except x and y are allowed, and no
literals (other than e, p and d if they are set to represent e,
π, and ° ) are allowed in the equation.
- polar graphs. Each equation produces one curve on the graph.
Each equation may be expressed in either explicit or implicit
form. No variables other than r (which represents the radius r)
and t (which represents the angle θ ) are allowed, and no
literals (other than e, p and d if they are set to represent e,
π, and ° ) are allowed in the equation.
For example, r + t = 5 and r = 5 − t will both produce (the same) spiral.
- parametric graphs. A pair of equations is required to produce one curve.
The first equation of the pair describes how x varies with the parameter t,
and the second one describes how y varies with t.
The equations must be of the form x = f(t),
y = g(t) where f and g are both functions of
t.
No variables other than x, y and t are allowed, and no
literals (other than e, p and d if they are set to represent e,
π, and ° ) are allowed in the equation.
An example is the pair of equations x = 4 cos(6.28 t), y = 2 sin(6.28 t)
which traces out an ellipse of width 8 and height 4, as t ranges from 0 to 1.
Graph Settings
The Graph window consists of the graph area, which is the main, upper-left area of the window
that contains the graph, and the Graph Settings frame, which is the gray area along
the right edge of the window.
You can get a description of each graph setting by clicking on it in the diagram below:
- These two values set the minumum and maximum
x coordinates displayed in the graph.
(Note that these values do not take effect until you click on the Apply Settings button).
- These two values set the minumum and maximum
y coordinates displayed in the graph.
(Note that these values do not take effect until you click on the Apply Settings button).
- Click on the up/down arrows to set the
line thickness of all the curves on the graph.
- Axis settings. Click on the Show Axes checkbox to
show or hide the axes. You have the option of displaying either frame style axes
(4 axes arranged around the graph like a picture frame) or cross hair style axes.
The values in the text boxes are used to set the number of divisions on the axes
(i.e. the number of tick marks minus 1).
(Note that these values do not take effect until you click on the Apply Settings button).
- Grid settings. Click on the Show Grid checkbox
to show or hide a grid of dots, a sample of which is shown in (12).
The values in the text boxes set the number of divisions to break the domain and range into.
(Note that these values do not take effect until you click on the Apply Settings button).
- Parameter t. You can plot one or more
pairs of parametric equations. Each pair produces one curve.
The pairs must all have the same minimum and maximum value of the parameter t,
which is set using the text boxes.
(Note that these values do not take effect until you click on the Apply Settings button).
Checking the Draw Dot checkbox displays a dot on the parametric curve at the current value
of parameter t. The current value of t can be varied by dragging the pointer on
the slider or by clicking the > (Play) button. Clicking Play a second time pauses the playback.
You can move the dot to another parametric curve by right-clicking on that
curve’s equation label and selecting “Move dot onto this curve” from the pop-up menu.
- Click on Apply settings to apply all your chosen settings.
This is the only way to make the values typed into the various text boxes take effect.
- Click on Factory settings to reset all settings to their defaults.
- Click on Copy to Workspace to copy the graph as it
presently appears back to the workspace.
- The equations for all the curves are also printed on the graph.
Initially these equation labels are floating in the upper left corner.
You can drag them anywhere you like, but once you do, they become anchored to
the new location. This means that if you pan or zoom, they could shift out of sight,
and you might have to drag them again to keep them in sight.
Right clicking on the equation label displays a pop-up menu that allows you to
change the color of the label (and graph),
delete the equation label, or move the parametric curve dot onto this curve.
- This is the point on the parametric curve for the shown value of parameter t.
Setting the value of t is described in (6) and
moving the dot onto another curve is described in (10).
- Click and drag the resize handle (the black square) to change
the size of the graph region.
- Right clicking on an equation label displays this pop-up menu.
From this menu you can change the color of the label (and graph), delete the equation
label, or move the parametric curve dot to this curve.
- Right clicking anywhere in the graph area displays the
Zoom and Pan pop-up menu. From this menu you can choose to zoom in (magnify)
or zoom out (from the center of the graph) by a factor of 2.
From this menu you can also select whether click and drag causes Zoom to Rectangle
or Pan. If Zoom to Rectangle is on, then clicking and dragging in the graph region
traces out a rectangle which then becomes the new graph area.
If Pan is on then clicking and dragging in the graph region shows
an arrow which indicates which way the graph area is “pushed ” in order to expose
some neighboring graph area.
- The status panel shows the coordinates of the mouse pointer.
Example
Try dragging the following example into the Algebra Coach.
It produces a parametric graph, a y versus x graph and a
polar graph all on a single plot:
x = t cos(t), y = t sin(t),
x + y = 2, r = 1 / sin(t) + 3