The Interactive Graph below needs the Java Plugin for your browser. Download it here. The plugin is perfectly safe. If you do NOT have the plugin you will not see the interactive graph within a large rectangle below the directions.

Please start with the video tutorial on the right to get some insight into the interactive Graph below.

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DIRECTIONS
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Below is the function f(x) = (1/2)^x.

- You will see a red point that you can manipulate with your mouse. You can drag the red point along the curve and see the points x value "projected" along the x-axis and the points y value "projected" along the y axis.

- Also, by right clicking your mouse on the graph you will bring up a menu system that allows you to adjust the Cartesian Coordinate System on which the interactive graph sits.

- Your goal is to be able to do the following:

a) Determine the domain by moving the red point and examining the projection of the x coordinate along the x axis.
b) Determine the range by moving the red point and examining the projection of the y coordinate along the y axis.
c) Determine on what intervals of x the function f(x) will be increasing or decreasing.

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INTERACTIVE TABLE AND GRAPH FOR y = (1/2) ^x
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The INTERACTIVE TABLE AND GRAPH below needs the LIVE MATH PLUGIN for your browser. Download it here. The plugin is perfectly safe. If you do NOT have the plugin you will not see the interactive graph within a large rectangle below the directions.

I suggest that you use Firefox for the greatest flexibility in using Live Math.

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DIRECTIONS
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Below is the function f(x) = (1/2)^x , a table of ordered pairs for the function, a graph of points defined by the ordered pairs in the table and an "interpolated" curve going through the points. You have a number of ways to interact with the module below. Let me explain:

a) You can change the values of the "domain" in the table. There are two numbers initially in the domain below -4 and 3. Note that the first number in the domain, -4, MUST be less than the second number, in this case 3. Go ahead and see what happens if you change the domain - don't go crazy with super large numbers!

b) Due to what seems like a programming bug in Live Math you can change how many points you want but the number of points must be less than or equal to the original number of points which is 8. Go ahead and see what happens if you change the number of points.

c) You can determine how your x values will get incremented by changing the value of "inc".
Go ahead and see what happens if you change "inc"- don't go crazy with a super large number!

... Left click this icon. The go to the graph, left click, hold and then drag around a region that you want to zoom-in on, i.e. get closer to the graph.

...Left click on this icon and you will zoom out, i.e. move further away from the graph.