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
- 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?
- 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?
- 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?
- 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.
- 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.
- Reset the Linear Transformer by clicking Delete All.
Click New to obtain the default function.
- Activate the Ghosts feature with the "2 seconds" option.
- Move the default function so its y-intercept is at (0, 8).
- 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?)
- 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)?