Function Analyzer: Warm-Up

It's always a good idea to "warm up" or acquaint yourself with a new software tool before using it with an activity. If you feel comfortable exploring the buttons and features on your own, feel free to do that. If you prefer a more structured exploration, try the activities below.

Click to open the Function Analyzer.

Note The Function Analyzer opens in a new browser window. As you explore the software, keep this window open for reference. Don’t modify the default function shown when you launch the Function Analyzer. The instructions below assume that the interactive appears as it does when it first loads.

Warm-Up A: getting started

The Function Analyzer doesn’t allow you to manipulate the graph directly. It lets you specify a value for the function for which you can identify the value of x that makes the statement true.

• Take a look at the software and familiarize yourself with the buttons. How many buttons are there? What guesses can you make about what they do?
• The Function Analyzer displays more representations of a function than most tools. How many different representations does it show and what are they?
• The Function Analyzer has three different symbolic expressions. How do they differ?

Warm-Up B : Try It and See

1. Look at the Algebra Tiles Model. The area model in the Function Analyzer represents the value of the function—f(x) or y—for a specific value of x.
   
   
   • Note the function and the value of x that is displayed by default when you launch the Function Analyzer.
   • The total number of tiles in the algebra tiles model should be the same as the value of the function when you plug in the value of x.
   • As you perform other tasks, observe how positive and negative values are represented differently in the algebra tiles model.
2. Use the Slider. Move the slider at the bottom of the graph. Observe the effects of using the slider in the following ways.
   
   
   • What happens in the graph?
   • What happens in the algebra tiles model?
   • What happens in the symbolic representations?
3. Edit the Symbolic Expressions. Try editing the symbolic expressions.
   
   
   • Which symbolic expression can you modify directly?
   • Which components of the symbolic expression can you select and how do you change those values?
   • As you change values in the symbolic representation, what happens to the graph? To the algebra tiles model? To the other symbolic representations?
4. Use the Tile Bin. Try clicking the various buttons in the tile bin.
   
   
   • What do the "x" and "" buttons do? The "1" button?
   • What do the "Positive" buttons do? The "Negative" buttons?
   • What does the "eraser" button do?
   • As you click buttons in the tile bin, what happens to the graph? To the algebra tiles model? To the other symbolic representations?
5. Experiment with Other Features. Try using the other buttons. Each time you try a new button, notice what changes.

Warm-Up C : Make It and Check It

Now you're ready to use what you've learned about the software to work with some specific functions, and see what you notice.

1. Reload the Function Analyzer.
2. Change the default function so that its slope is 1.5 and its y-intercept is (0,1).
3. Change the value of the equation to 4.
4. Use the slider to find the value of x that solves the equation.
5. With the slider at the solution, check that the number of tiles in the algebra tiles model equals the value of the equation.