Mathematics Education

EMAT 6680 Assignment 0

Last modified on July 3, 2008.

In the following, where you examine multiple graphs, consider the different impact and observations you can make by a sequence of graphs, adding one graph at a time, in contrast to creating all graphs in a set at once.

This assignment is quite easy with Graphing Calculator 3.5. Items 1 to 5 could be accomplished, with some modification, using a TI-81, TI-82, TI-83, TI-84, etc.

Items 6 - 10 take advantage of graphing relations as contrasted with graphing functions.

No Write-up required for Assignment 0. Experiment with Graphing Calculator 3.5, xFunction, and hand calculators.

1. Graph the following on the same axes:

Observations? Think about the difference, for students, of graphing all at once, versus adding one equation and graph at a time.

2. Graph the following on the same axes:

Observations?

3. Graph the following on the same axes:

Observations?

Contrast the set of Graphs in Item 4 and the set of Graphs in Item 5.

4. Graph the following on the same axes:

Do an animation driven by n from the following:

5. Graph the following on the same axes:

Do and animation driven by n from the following:

6. Try:

Observations? For what values of n does

produce a graph? Do an animation driven by n for the range of values where n produces a graph.

What if:

Try the range of n from -2 to 2 in 100 steps.

Try graphing all of these equations on the same set of axes. Adjust the zoom in and out. One picture is

7 Graph the equation:

Adjust the zoom in and out to get interesting patterns. Try setting the equation equal to n and animate from 0 to 2.

8. Try:

for different values of A. You might also try different screen sizes, zooming in, or zooming out.

9 Try:

Then replace the 5 in each side of the equation with other small values. You may have to re-size your graph. It is more interesting if you keep multiple graphs on the same axes or try an animation.

10. Consider the polar equation

Graph the equation for n = 5 and n = -5. One should be a heart, one should be a bell.

On the same set of axes, make graphs for n = -5, -4, . . . 4, 5 (that is, 11 graphs). You may want to size your window from -5 to +5 on each axis.

Graph the equation and use the animation feature in Graphing Calculator to let n range from -5 to 5.

Experiment a bit.

What if the equation was written with the sine function rather than the cosine function?

What about other ranges for n?

Consider other equations.

11. One strophoid has the equation:

Graph it. Try replacing the 5 on the right hand side by other values. Try replacing the 5 on the left hand side with other values. Both? What if x is replaced by x-2? What if x is replaced by sin(x)? y by sin(y)?

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