Linear Transformer: 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 Linear Transformer and then do the activities below.

Note The Linear Transformer opens in a new browser window. As you explore the software, keep this window open for reference.

Warm-Up A: getting started

Take a look at the software and familiarize yourself with its functions.

• How many buttons are there? What guesses can you make about what they do?
• Look at the graph. Describe the line that appears when the program opens.
• Find the symbolic expression at the right. What is this default function?

Warm-Up B : Try It and See

1. Manipulate the Graph. Click the red line on the graph and drag it around.
   
   
   • What changes and what stays the same in both the graphic and symbolic representations?
   • Is there a difference in the effects of dragging the line horizontally and vertically?
2. Use the Pushpin and Ghosts. Activate the Pushpin by selecting the checkbox.
   
   
   • Click and drag anywhere on the line (except at the pushpin's location). What happens to the graph? How does the symbolic expression change?
   • Click and drag the pushpin to a new location.
   • Click and drag the line again. What do you notice?
   • Activate the Ghosts feature by selecting either "2 seconds" or "persistent" in the pull-down menu. Click and drag the line again. What do you notice?
3. 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 when you move the slider?
   • What does the rectangle to the left of the graph do in relation to the action of the slider?
4. Edit the Symbolic Expressions. Experiment with changing the symbolic expressions in the tasks below.
   
   
   • How do you choose which form of the linear function to view and modify?
   • Which components of the symbolic expression can you select in the slope-intercept form? Experiment with changing values in the slope-intercept form and observe corresponding changes in the graph.
   • Which components of the symbolic expression can you select in the point-slope form? Experiment with changing values in the point-slope form and observe corresponding changes in the graph.
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 Move It

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

1. Reset the Linear Transformer by clicking Delete All.
   
   Click New to obtain the default function.
2. Activate the Ghosts feature with the "2 seconds" option.
3. Move the default function so its y-intercept is at (0, 8).
4. Change the slope of your function to 1.5 (keep the y-intercept the same). (Hint: There are two ways to do this. What are they?)
5. Duplicate the function.
   
   • Reflect this new function about the x-axis.

     Which symbolic expression describes the reflected image? How does it compare to the symbolic expression for the function you just reflected?

   • Now reflect the new function about the y-axis.

     Which symbolic expression describes this reflected image? How does it compare to the symbolic expression for the function you started with (in this task)?