Graph Sketcher

What is Graph Sketcher?

This activity allows the user to see functions typed in as algebraic expressions graphed on the coordinate plane.

The software graphs functions in basically the same way we would do it on paper. Axes are drawn, and a scale is set - based on the input in the range boxes. Next a table of x values between the two specified limits is generated, and then corresponding y values are calculated. Points are plotted; dots are connected; and the graph is displayed.

So what is different? Here is the big difference in the way the software works: We would probably plot 5 to 10 points and use our "math intuition" to connect the points appropriately. The computer plots many more points (depending on the x range, somewhere around 100) and connects the dots. This is how graphing calculators work, too.

This can lead to interesting behavior for certain functions. Polynomials like lines and parabolas will graph just as they should. Other functions, such as those for which x appears in a denominator, may have places on the graph where the computer has trouble plotting them correctly. This leads to the following moral:

Related Resources

• Activity Conic Flyer
• Activity Data Flyer
• Activity Function Flyer
• Activity General Coordinates Game
• Activity Graphit
• Activity InteGreat!
• Activity Maze Game
• Activity Ordered Simple Plot
• Activity Scatter Plot
• Activity Simple Coordinates Game
• Activity Simple Maze Game
• Activity Simple Plot
• Activity Slope Slider
• 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 Graph Sketcher Suggestions
• Worksheet Graph Sketcher Suggestions (doc)

How Do I Use This Activity?

This activity allows the user to see functions typed in as algebraic expressions graphed on the coordinate plane.

Controls and Output

• Type the formula of the function you want to graph in the space at the bottom of the applet, next to y(x)=.
• 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

  * When x is less than zero, the exponent must be written as a whole number or in fraction form, not a decimal. For instance, if you want to graph the fifth root of negative numbers, you must write x^(1/5), not x^(0.2).
• Click Graph to graph the function.
• To plot more than one function on the same graph, separate the functions with commas. You may plot up to ten functions.
• 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.
• There are three radio buttons that allow you to display no grid lines, light grid lines or dark grid lines. Select the radio button next to the type of grid line you would like to view. Check the box next to Hide Grid to hide grid lines. Grid lines are drawn on the x-axis at intervals of x-scale and on the y-axis at intervals of y-scale.
• To find a position on the graph you can click with the mouse. The (x,y) pair where you clicked will appear in the Mouse Position 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.
• 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.
• Show Tabular Function Data