Plotting the range of a 2D graph

[cliverlong]

Hi,

In Autograph I can easily control the domain of a graph by adjusting the settings. I can also get the graph to be traced out as the x value increases by using the turtle and changing speed by adjusting the x-increment.

I would like to show the range on the y axis for say y = x^2 - 4, effectively just plotting the points (0, y-coordinate of curve) . Animation in time with the actual curve plotting would be good but not necessary. I have tried plotting a parametric equation x = 0 , y = a and animated the variable a for the range I wanted but nothing appeared. Of course, I would really want the y value to be the y value of the function. Any suggestions?

Thanks

Clive

[Support]

Hi Clive,

The way I would do this is as follows:

1. Select the curve y = x² - 4 and click Enter Coordinates. Enter a point with x coordinate x = a.

2. Make sure nothing is selected and enter another coordinate. This time with coordinates (0, a² - 4)

3. Open the Constant Controller and adjust the value of a, you will see two points moving, one showing the position of the point on the curve and one showing the y-value of that point on the y-axis.

Best regards,

Simon

[cliverlong]

Seems obvious. can't see how I missed that.

Thanks

Clive

[cliverlong]

A variant/ development of your solution (I will load this up in the appropriate place - where is that?)

I will check these instructions - but this is the essence

1. Defined the curve , say y = x^2 - 4
2. Selected curve then right-clicked and "entered point on curve" with, say x = -2
3. Drew horizontal line through the point on curve
4. Inserted point on y axis where horizontal line intersects (forgot exactly how I did that)
5. Hid the horizontal line
6. Selected point on curve and point on y-axis and inserted line segement between them, changing the line to a dotted line
7. Set trace on point on vertical y-axis
8. Selected the point on curve and moved it using the left and right arrow keys
9. As the image point on y-axis moves it traces out the range for whatever is the corresponding x-value (domain )
10. Obviously the trace of point on y-axis will only ever show a finite range (useful when you have a restricted domain) and a bit of hand-waving needed to justify what the domain should look like for x across all reals.

Interesting how many words needed to try to convey what a clear Autograph shows.

Clive

[cliverlong]

Attached is a simple .agg file using trace of image point on y-axis to show domain as point on curvehas its x value changed.

  simple domain-range example using trace.agg (Size: 4.78 KB / Downloads: 5)
Moving the point on curve achieved by selecting it then moving it using the left and right arrow keys.

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Attached is a screen image of the range shown as purple trace on y-axis for an x domain of -3 < x <-1 .

  domain range autograph image.doc (Size: 26.5 KB / Downloads: 5)
I put the info in two posts because I couldnt get the emf file to attach to previous post. I embeddeded the image within a .doc format which seems to have worked.

<< added >> I can Edit the equation of the curve, say make it a cubic x^3 - x^2 -2, and since the point is defined as a point on the curve, and the point on the y-axis lies on the horizontal line from the point on the curve, the x-value is unchanged and the point remains on the new curve and the line segment between curve and y-axis is still visible. I have to "reset" the trace on the point on the y-axis, reselect the point on the curve and start moving the point (on curve) to see the range for the new curve. Not particularly sophisticated, but it seems robust and clear enough for my needs.

Clive

[Support]

Hi Clive,

Fantastic enhancement to make the solution more generic, thank you for sharing that.

Simon