Exponential Functions

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Author: chris ludbrook

Description:

1. Graph exponential functions by manipulating the graph of the parent function.

We have spent a great deal of time discussing functions and their graphs and we have learned how various graphs behave as variables in the functions change. The simple exponential functions we will examine involve raising a base value to a variable.

For instance is a fairly simple exponential function. As you might suspect, the graph of this function becomes steeper as the values for x increase and less steep as the values for x decrease. We will examine the behavior of these functions as various components of the functions are manipulated and we will seek to develop an understanding of the patterns so that we can simply manipulate our original graph instead of replotting points for each situation.

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Tutorial

Creating Sliders to Examine Exponential Functions

Sliders are gadgets in Geogebra (or any similar software) that allow you to change the value of a variable in an equation without having to change the variable by hand multiple times. You simply "slide" the button and the value of the variable changes as does the corresponding graph.

Creating sliders is rather easy. Just follow the set of steps below and you'll be graphing exponential functions in no time.

1. Open Geogebra and select the slider button.

2. Click anywhere on the graph section of Geogebra. You can move the slider

later if it is in the way. You can name the slider anything you want, but in

this case, name it "b" and select Apply.

If the preset Interval in the slider does not provide the values you need, simply right click on the slider at any time and select "Object Properties" to change the Interval values.

3. Now type an exponential function into the input bar in the form y=b^x.

4. You can now use the slider to change the value of the base. It is important

to remember that you must select the "Move" icon to change the value

of the slider.

5. Now continue the exercise using the Graphing Exponential Functions OneNote and add additional sliders as indicated.