Graphit

What is Graphit?

This activity allows the user to plot ordered pairs and algebraic functions on the same coordinate plane. It combines the capabilities of Simple Plot and Graph Sketcher ( See the Learner tab for additional information).

The Cartesian coordinate system was formalized by Rene Descartes in the 17th century to help visualize functions via plotting function values as ordered pairs. In this system a grid of evenly spaced horizontal and vertical lines is drawn, a center or "origin" is chosen, and horizontal and vertical scales are chosen. Here's an example:

Another name for the horizontal movement value is the abscissa, and the vertical movement is the ordinate. These terms are more rare now than they used to be, but you might still hear them being used.

Related Resources

• Activity Algebra Four
• Activity Algebra Quiz
• Activity Data Flyer
• Activity Function Flyer
• Activity Function Machine
• Activity General Coordinates Game
• Activity Graph Sketcher
• Activity InteGreat!
• Activity Linear Inequalities
• Activity Maze Game
• Activity Multi-Function Data Flyer
• Activity Ordered Simple Plot
• Activity Parametric GraphIt
• Activity Scatter Plot
• Activity Simple Coordinates Game
• Activity Simple Maze Game
• Activity Simple Plot
• Activity Slope Slider
• Activity Whole Number Cruncher
• Discussion about From Graphs to Function Machines and Back
• Discussion about Gathering Information from Graphs
• Discussion about Introduction to the Coordinate Plane and Coordinates
• Worksheet Four Quadrant Grid, 14x18
• Worksheet Four Quadrant Grid, 28x36
• Worksheet Functional Graphs Worksheet
• Worksheet Functional Graphs Worksheet (doc)
• Worksheet Graphit Answers Exploration Questions
• Worksheet Graphit Answers Exploration Questions (doc)

How Do I Use This Activity?

This activity allows the user to plot ordered pairs and algebraic functions on the same coordinate plane. It combines the capabilities of Simple Plot and Graph Sketcher.

Controls and Output

• The area at the top of the screen is where the plot is displayed.
  

• The Function area is for entering functions. To graph a function, type the formula of the function you want to graph in the space at the bottom of the applet, next to y(x)=. You may graph up to nine functions on the same plot. Enter one formula per line, as shown.

  

  Basic functions and their compositions can be typed as follows:

  Function	Symbol	Examples (including combinations of functions)
  addition	+	x + 3 x plus three
  subtraction	-	5 - x five minus x
  multiplication	*	(x - 2)*x x times x minus two
  division	/	3/x three divided by x
  power	^	x^3 - 1 x to the power of three minus one
  power	**	x**3 - 1 x to the power of three minus one
  (pi)	pi	sin(pi*x) sin of (pi) times x
  square root	sqrt(...)	sqrt(x-1) square root of x minus one
  nth root (see * below)	x^(1/n)	x^(1/3) cube root of x
  absolute value	abs(...)	abs(3 - x) absolute value of three minus x
  e to the power of x	exp(...)	exp(x) e to the power of x
  sine	sin(...)	sin(x**2) sine of x squared
  cosine	cos(...)	cos(5 - x) cosine of five minus x
  tangent	tan(...)	tan(x) tangent x
  arcsine	asin(...)	2*asin(x) two times arcsine x
  arccosine	acos(...)	acos(x) arccosine x
  arctangent	atan(...)	atan(x) arctangent of x
  hyperbolic sine	sinh(...)	sinh(1 - x) hyperbolic sine of one minus x
  hyperbolic cosine	cosh(...)	cosh(10/x) hyperbolic cosine of ten divided by x
  hyperbolic tangent	tanh(...)	tanh(x) hyperbolic tangent of x
  natural logarithm	ln(...)	ln(x) natural logarithm of x
  base 10 logarithm	log(...)	log(x + 5) base ten logarithm of x plus five

• The Data area is for entering data points. Data points should be in the form (x, y). Parentheses around the data point are optional. A tab or a space can separate the x and the y though no space is needed. A space or a carriage return is required to separate the data points from one another. After you input the coordinates, you must press the Plot/Update button to graph them.
• If you have trouble copying data from the applet and pasting it into an Excel spreadsheet, please see our Excel Copy/Paste Help.
• You can plot a total of nine functions at once. You can also plot a total of twelve data sets at once. Separate each function with a comma. Separate data sets by typing newgraph on a line by itself in the Data window. If you want to specify your own colors for the graphs you can replace newgraph with the following keywords: bluegraph, redgraph, greengraph, blackgraph, graygraph, magentagraph, browngraph, orangegraph, purplegraph, crimsongraph, darkbluegraph.
• You can choose from two plot types. "Connected" draws a line from one point to the next (before the line is drawn the points are sorted by their x coordinates.) "Scatter Plot" just draws the points as dots on the graph. These options do not affect the way functions are graphed.
  
• Click Set Window to determine how the coordinate plane will appear on your screen. A new window will open that allows you to change the setttings. X min and X max are the minimum and maximum x-values displayed on the graph. Similarly for Y min and Y max. X scale is the distance between vertical gridlines if Choose Scale Automatically is checked. Y scale is the distance between horizontal gridlines if Choose Scale Automatically is checked. If the Use Defaults box is unchecked, Graphit will choose appropriate values for you. If you uncheck that box, you can override Graphit's values with your own. If you wish to revert back to the default values, click Get Defaults in the Set Window box. Click Set to make the changes to the window parameters take effect.
  
• You can choose what you see on the graph. You can select to show all functions, all data, and/or the grid lines by checking the appropriate box or radio button in the Show box.
  
• The applet also can tell you the location of any click. Just click the mouse anywhere on the graph that you want to know the coordinates of and the coordinates will appear in the Mouse Pos. box.
  
• 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, then click and drag over the area of the graph for which you wish to zoom to. Note that after clicking and dragging over the selected area, the zoom in button is automatically released.
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  • To zoom out, simply click the middle button. 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.
  • Auto Scale: Checking the Auto Scale check box gives 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.