 # EMAT 4680/6680 Explorations 00

The primary purpose of this page is to provide a range of investigations to allow you to explore the features of Graphing Calculator 3.5,   Graphing Calculator 4.0,    Graphing Calculator 4.0 Lite, or other graphing technology.

As an alternative you might want to learn the features of Geogebra 5.0.    This is a powerful FREE software that is gaining lots of use in schools.    And, on the internet, check out Desmos.    Desmos is also a free but web based software and has many interesting features and examples.

In the following investigations, 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, 4.0, or 4.0 Lite. Items 1 to 5 could be accomplished, with some modification, using a TI-81, TI-82, TI-83, TI-84, TI - 85, TI-89 or n-spire or using other graphing software.

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

No Write-up is required for Assignment 0. Experiment and learn the features of Graphing Calculator, Geogebra, or Desmos software and hand calculators. 1. Graph the equations at the right 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.

Graph an animation with GC 3.5 or GC 4.0, letting n range from - 4 to 4 using the equation

y = x + n

Think about when there would be a purpose to use an animation over a range rather than showing multiple graphs. 2. Graph the equations at the right on the same axes:

Observations?

Graph an animation with GC 3.5 or GC 4.0 of

y = (x - 2) + n

for a range of n. 3. Graph the equations at the right on the same axes

Observations?

Animate y = n(x - 2) with GC 3.5

Contrast the set of graphs in Item 4 and the set of graphs in Item 5. 4. Graph the equations at the right on the same axes:

Do an animation driven by n from the following:  5. Graph the equations at the right on the same axes:

Do an 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.  This picture is for a small piece of the plane and for a very restricted range of A.  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.   Use Graphing Calculator to graph the 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).

See Desmos Heart to Bell
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)?