Data Flyer

What is Data Flyer?

This activity allows the user to plot a set of (x,y) ordered pairs and graph a function on the same coordinate plane. The applet allows the manipulation of a function of the form y = f(x). Using slider bars one can manipulate the function to change the constant values and view the effects of those changes.

The user can explore the effect of changing constants in most types of functions including:

• linear
• quadratic
• exponential
• trignometric

The sum of the squares of the deviations is shown to assist the user in determining how well the function fits the data. As a general rule of thumb, the smaller this value, the better the curve fits the data for that type of function. However, this value implies little about the goodness of fit between different functions.

Related Resources

• Activity Conic Flyer
• Activity Derivate
• Activity Function Flyer
• Activity Graph Sketcher
• Activity Graphit
• Activity InteGreat!
• Activity Linear Inequalities
• Activity Multi-Function Data Flyer
• Activity Multiple Linear Regression
• Activity Simple Plot
• Activity Slope Slider
• Discussion about From Graphs to Function Machines and Back
• Discussion about Functions as Processes or Rules: "Function Machines"
• Discussion about Independent and Dependent Variables
• Discussion about Introduction to the Coordinate Plane and Coordinates
• Worksheet Data Flyer Exploration Questions
• Worksheet Data Flyer Exploration Questions (doc)
• Worksheet Four Quadrant Grid, 14x18
• Worksheet Four Quadrant Grid, 28x36

How Do I Use This Activity?

This activity helps the user to visualize the concept of equivalent fractions. The user has to illustrate two fractions which have the same value as a third given fraction.

Controls and Output

Find out how to...

The area in the center of the screen is where the plot is displayed.

Grid Lines

• There are three types of grids: No Grid, Light Grid Lines, and Dark Grid Lines. To activate any of these three options, highlight the circle next to the appropriate option:

No Grid graph:	Light Grid Lines graph:	Dark Grid Lines graph:

The Interactivate graphing activities allow three ways to alter the range on the axes.

1. Setting exact values for axis mins/maxes: You may set the graph boundaries by clicking the Set Window button and entering new values for the x max, x min, y max, or y min. Then click the Set button to set the boundaries. To return the values to their defaults, you click the Get Defaults button and then click the Set button again. If you do not want to change the window settings you may click Cancel.
2. Zoom/Pan buttons. In the upper right corner of the graph, there are three buttons with pictures of magnifying glasses. From top to bottom these buttons represent zoom in, zoom out, and pan, respectively.
   • To zoom in, click the top button to depress it, then click and drag over the area of the graph that you wish to magnify. The images below show first the process of dragging a box around a desired zoom area with the mouse (left), and then the resulting zoomed image after the mouse button is released (right). Note that after the zoom-in has been performed, the zoom-in button at top right is no longer depressed.
   • To zoom out, simply click the second of the three zoom buttons. The graph will automatically zoom out by doubling the min and max values of the axes.
   • To use the pan feature, click the bottom magnifying glass button to depress it. Click and drag over the graph and the graph will pan around according to the movement of the mouse. Upon releasing the mouse, the pan button is released.
3. Auto Scales: Checking the Auto Scale check box gives you the smallest window possible so that all of the data points still fit on the coordinate plane. Note that there must be data for this feature to work.

• Checking the Show Trace box will cause old graph lines to remain visible (in a lighter color) as you change the function by moving the sliders. To remove the trace, click the clear trace button. To stop the tracing, uncheck the Show Trace check box.
• When Show Trace is checked, you will be unable to Plot Data, Show Squares, Auto Scale, Show Vertical Asymptotes, use the pan/zoom features, or change the darkness of the grids. When any of these options are checked, you will be unable to Show Trace.

• You may see the vertical asymptotes of a graph (if there are any) by checking the Show Vertical Asymptotes check box. For example, the tangent graph with this option selected looks like:

  

  * Note that due to the programming technique used to detect asymptotes, this program will only detect those asymptotes that go from a large positive y value to a large negative y value at the discontinuity. f(x)=log(x) is an example of a vertical asymptote Data Flyer will not detect.

• The Data area is for entering data as ordered pairs. You enter the ordered pairs by separating the x and y of the ordered pair with a comma, a space, or a tab, and putting each ordered pair on a separate line. Most browsers will allow you to cut and paste data from two columns of a spreadsheet application or html table.
• After entering the data, plot it by pressing the Plot Data button.
• You may clear the data by clicking the Clear Data button.
• If you have trouble copying data from the applet and pasting it into an Excel spreadsheet, please see our Excel Copy/Paste Help.

Graph Functions

• Data Flyer allows you to enter an algebraic function in the box labeled f(x)=. For information on the syntax of entering functions and numbers with scientific notation, see Interactivate Functions Help.
• Note that numerical values entered should be accurately calculated from 10 ^-8 to 10 ⁸ . Numbers larger or smaller than these values produce unreliable results. If you enter a number with a magnitude smaller than 10^-6 or larger than 10^6 it will automatically be converted to scientific notation.
• Enter the function you want to graph in the box marked f(x)=. Any constant or coefficient you wish to manipulate must be entered as a number. For instance, if you wish to experiment with the linear function f(x) = x + 8 and wish to manipulate the coefficient of x it is necessary to type the equation as f(x) = 1*x + 8 so the computer recognizes the multiplier as a parameter. Likewise if you want to experiment with the sine function f(x) = sin(x) and be able to manipulate the parameters such as the y-intercept, phase, frequency, and amplitude, it is necessary to type 1*sin(1*x+0)+0. (Try typing in both and clicking the set function button so you can see the difference.)
• Once you have set the function you may enter a different function by clicking the Change Function button, entering the new function and clicking the Set Function button again.

• To view a table of values corresponding to the graphed function, click the Show Tabular Data button.
• The x values in the table increment equally and then give the corresponding f(x) values for the function. You can change these data values by entering a new minimum x value, new maximum x value, and step size. If you enter a step that does not divide evenly into the range, the table will stop at the greatest multiple of the step that is less than the maximum. The precision field allows you to adjust the number of decimal points to print out values of x and f(x).

• You may set the sliders back to the original values that they had when the the function was entered by clicking the Reset Sliders button.
• The Slider Limits button brings up a dialog box that allows you to set the minimum and maximum values of each slider bar. You can also set the step size for each slider bar. The step size determines how precisely you can control the value of the constant. For instance, if you set the minimum to 0, the maximum to 1, and the step to 0.1, moving the slider will step the constant from 0 to 0.1 to 0.2, and so on. However, if you set the step to 0.2, the slider will step the constant to 0, 0.2, 0.4, etc.
• The number of increments must be smaller than 100. If you enter parameters such that the number of increments is greater than 100 then an error message appears asking you to readjust by changing the slider min, slider max, or step size.
• Checking the Exponents Change box before clicking Set Function will allow you, after the function is graphed, to use slider bars to adjust the values of any exponents.

• The sum of squares of deviations is shown at the top of the applet. The closer this number is to zero the more accurate your function is in relation to your data. You may see a data table of these deviations by clicking the Show Deviations button.
• Checking the Show Squares check box draws squares from the data points to the function on the coordinate plane. The length of each side of the square is equal to the vertical distance from the coordinate to the function value at the x-value of the coordinate.
• Decreasing the sum of the squares of the deviations between the points and the function (think of decreasing the sum of the areas of the squares shown above) produces a better "fit" of the function to the data. Experiment by moving the sliders from side to side until you find a value that you think minimizes the sum of squares of deviations:

Description

This activity allows the user to plot data points and a function on the same coordinate plane. This activity would work well in groups of three to four students for about 45 minutes if you use the exploration questions. Time will also vary depending on how many data sets you use.

Place in Mathematics Curriculum

This activity can be used to:

• Develop understanding of the Cartesian coordinate system
• Explore how changing coefficients affects the shape of a graph.

Be Prepared to

• explain how to decide what type of relationship a set of data have
• give examples of real world situations where people try to fit a line to a set of data
• generalize the effects of changing the constants in the type of function the students are studying

Related Resources

• Activity Conic Flyer
• Activity Derivate
• Activity Function Flyer
• Activity Graph Sketcher
• Activity Graphit
• Activity InteGreat!
• Activity Linear Inequalities
• Activity Multi-Function Data Flyer
• Activity Multiple Linear Regression
• Activity Simple Plot
• Activity Slope Slider
• Discussion about From Graphs to Function Machines and Back
• Discussion about Functions as Processes or Rules: "Function Machines"
• Discussion about Independent and Dependent Variables
• Discussion about Introduction to the Coordinate Plane and Coordinates
• Lesson on Cartesian Coordinate System
• Lesson on Graphing and the Coordinate Plane
• Lesson on Graphs and Functions
• Worksheet Data Flyer Exploration Questions
• Worksheet Data Flyer Exploration Questions (doc)
• Worksheet Four Quadrant Grid, 14x18
• Worksheet Four Quadrant Grid, 28x36