Grapher HowTo

Grapher - How To

Apple’s Grapher ApplicationTerry LindenmuthFebruary 8, 2009

Return to INDEX Draft 01/19/2010

Terry Lindenmuth INDEX Apple’s Grapher, Page 1

Index

Finding the Grapher ApplicationNew GraphSetting Up a 10X10 GridCaution: Spaces are interpreted as multiplication.Equation PaletteBuilt-In DefinitionsInsert text on the graphInsert screen captures on the graphScreen CaptureGroups to OrganizeGroups & Families of Equations (parameter)Changing the Coordinate SystemEquations in Non-Function FormPlotting PointsLinear Regression (Interpolation)Change Style - Color and LineEvaluating a FunctionIntersection(s) of two FunctionsInequalitiesRoots (Zeros) of a FunctionIntegration of a FunctionPolar GraphsSwitch 2D to 3DLocal Extremum and Inflection Pts. of a FunctionGraphing Piecewise Conditional Functions



Finding the Grapher Application

Method 1: The Grapher application is stored in Applications > Utilities > Grapher.app. After locating the “Grapher.app”, create a shortcut on your Dock.

Caution: If you move the application from the Utilities folder, the application does not always work properly.

Method 2: Use your Spotlight. Type in “Grapher.”

Look for

Method Visual:



New Graph

2D Graph or 3D GraphBefore you select open you should click on each option under 2D to explore what types of graphs are available. Then do the same thing with the 3D formats. You should begin with a format that is familiar. 3D graphing is often not intuitive to those who never worked in this environment.



Setting Up a 10X10 Grid

Setting Up a 10X10 Grid: For most introductory graphing students are use to seeing a 10 X 10 grid. To set the x-axis window, double click on a value on the x-axis. A drop down menu allows your to specify the range of values. Un-checking the “Adjust automatically” allows you to set the Major units. Major units are the numbers displayed as the axis labels. The Minor units is the number of tick marks between the Major units.Setting Up a 10X10 Grid continued on next page.



Setting Up a 10X10 Grid continued:Repeat the process to set up the y-axis.

You cannot set this as a default. To use this as a default Grapher window, save it with a name like, “Grapher10X10.gcx”. Then open this file to start the Grapher application.



Caution: SpacesCaution: Spaces are interpreted as multiplication.Do not add extra spaces. Spaces are interpreted as multiplication.Graph:

The first equation below is correct.The second equation has a space between the “x” and the “+4”. This is interpreted as (2x/3)*(+4).



Equation PaletteYou can get to the “Equation Palette” using the Window pull down menu.

Or you can use the keyboard short cut:

Or

Equation Palette Continued on next page.



Equation Palette Continued:When you are creating or editing an equation, simply click on a choice in the pallet and it will be placed into the equation.Check out all your choices:



Built-In Definitions“Help” is an unusual place for the “Built-In Definitions.” First time users may not think to look here. Please note that these are not clickable as are the items in the “Equation Palette”, but instead indicate the syntax for entering the constant or function.



Insert text on the graphInsert text on the graphSelect “Insert Text” from the “Object” pull-down menu. This creates a movable text box on the graph. Enter text.

With the text box selected you can now format the Text Box using the “Format” pull-down menu.



Insert screen capturesInsert screen captures on the graph. If you place a screen capture onto the clipboard (see next page), you can click onto your graph and paste.You can screen capture the equations in the left column of grapher and then paste them onto the graph (see yellow). You can then drag them anywhere on the graph. If you paste from the clipboard, make sure you are clicked on the graph and not the equation edit sections. The picture of the double conic was created in 3D, screen captured, then pasted onto this graph. The red text was created using the “Object>Insert text” feature.



Screen CaptureScreen Capture



If want to take a quick screen shot of something you see on your screen, hold down Command Shift 4 (all simultaneously.) This will allow you to draw a box of what you want to capture of the screen and it will save it as a graphics file on the desktop of your computer. Additionally, if you would like to skip a step and have the contents of your screen capture go directly to the clipboard, add the Control key to the keys. So, if you type Control Command Shift 4, you can select whatever you want on the screen and it will automatically be on your clipboard. Simply paste in whatever application you want (command v).

Command Shift 4 (all simultaneously.) Control Command Shift 4

Groups to OrganizeGroupsYou can organize you work by using “Groups.” Use either the “Equation” drop down menu or the “Wheel” in the bottom left to create a group. Click on the title bar to rename. Drag equations onto the group name. Drag equations into new locations within the group.

You can now hide or show the members of a group by clicking on the triangle in front of the group name. You can select or deselect the entire group with one click on the box in front of the group name. You can also select or deselect members of a group individually.

Note: Renaming a group is only available in Leopard.



Groups & Families of EquationsGroups & Families of Equations (parameter)

Under the “Powers of x” group two equations were entered; j={1,2,3} and y=x^j. The sub-group; j=1,j=2,j=3 is created by Grapher and graphs three equations.

Try this as an alternate approach.

Be sure to use braces.



Changing the Coordinate SystemChanging the Coordinate SystemAn exponential equation that is graphed on linear-log paper results in a straight line.

Enter the exponential function y = 3x

Using the “Format” pull-down menu change the coordinate system to linear-log.

Equation on left is Lin-Lin and the equation on the right the same equation on a Lin-Log coordinate system.

This would also be a good technique to examine a set of data points to help determine is an exponential function is an appropriate model for data.

Example 2: An power equation that is graphed on log-log paper results in a straight line.Enter the following equation and change the coordinate system

to Log-Log and visually verify it is a straight line.



Equations in Non-Function FormEquations in Non-Function Form

You can enter equations without starting “y =”. Simple delete the “y =” in the equation editor and enter you equation in non-function format. Enter the equation for this circle: x2 + y2 = 4

If the circle looks like a ellipse press:

The visually squares off the viewing window.The disadvantage is that certain features like “Find Intersection” will no longer be available. “Find Intersection” will work when equations are solved for “x”, and entered as “x =”.



Plotting PointsPlotting PointsFrom the “Equation” pull-down menu, select “New Point Set.”

Select “Edit Points”

Click on Column 3 and delete.Edit as needed.

Edit the name of the “Untitled Set” Continued...



Plotting Points Continued

With this highlighted click on the Inspector.

Make changes as needed. Uncheck “Polygon” to show points that are not connected with line segments.



Linear Regression (Interpolation)Linear Regression (Interpolation)

Select a point set.

Select “Interpolation”.

Select “Interpolate”.

Select “Stroke” to have the equation added to your equation list.

Close the pop-up window. You can now select the regression equation from the equation list.



Change Style - Color and LineChange Style - Color and Line

Select an equation from the equation list.

Select the inspector.Select the line color swatch to get the “Color” pop-up window. Click on a color or drag it

to the color swatch. You sometimes must click the refresh icon.Click on the zig-zag line icon to get the “Line Styles” pop-up window.

Close the pop-up windows when finished.



Evaluating a FunctionEvaluating a FunctionSelect the function in the list. Use the “Equation” pull-down menu to select “Evaluation.”

Enter a value in the “x = box” and observe the “y” value.

Keep or uncheck the display boxes. Hitting “Stroke” will generate equations in the list for the last three check boxes (if checked). Here are the Tangent and Perpendicular:



Intersection(s) of two FunctionsIntersection(s) of two FunctionsSelect the two equation in the “Equation” list. Select the first equation, then hold down the command key to select the second. With both equations selected use the “Equation” pull-down menu and select “Intersection”.

Enter a value for “x” near the point of interest. Clicking on the graph near the point of interest will also work.

You can screen capture the (x, y) location, close the pop-up window, and paste it onto your graph.Repeat the process to get additional points of intersection.



InequalitiesInequalities

I suggest entering both the inequality and the corresponding equation. You can use the option key to get the “or equal to”, but the graph looks the same.

Select one of the equations in the list. Select the “Inspector” to change the color and opacity.

continued…



Inequalities continued

Select one of the equations that goes with an inequality.

Select the “Inspector.”

Change the color and line stye to match the inequality.

You can find intersections of the equations, but not the inequalities.



Roots (Zeros) of a FunctionRoots (Zeros) of a FunctionEnter the function and press return to graph. Select the function in the equation list.

From the “Equation” pull-down menu select “Find Root.” Enter a value for “x” or click on the graph near the root of interest. The solution of “x” is given. The value for “y” is often given as an approximation of “0”.



Local Extremum and Inflection Pts. of a FunctionRoots (Zeros) of a FunctionEnter the function and press return to graph. Select the function in the equation list.

From the “Equation” pull-down menu select “Find Root.” Enter a value for “x” or click on the graph near the root of interest. The solution of “x” is given. The value for “y” is often given as an approximation of “0”.



Integration of a FunctionIntegration of a FunctionEnter the function and press return to graph. Select the function in the equation list.

From the “Equation” pull-down menu select “integration.”

Enter the lower and upper value and then press “Calculate.”

You can “Remove Integrated Area” in the “Equation” pull-down menu.



Polar GraphsPolar GraphsAt the 2D start-up screen select “Polar”.

Enter an equation “r =”. You can get theta from the equations pallet.



Switch 2D to 3DSwitch 2D to 3DYou can start a graph in 2D and switch to 3D and back to 2D. Here is a 2D equation of

an ellipse and itʼs 3D counter part.



Graphing Piecewise Conditional Functions

You can enter a piecewise function with this format:

y = condition ? expression1 : expression2

or

y = condition : expression1 : expression2

In these examples, expression1 is used if the condition is true. Otherwise, expression2 is used. You can leave out expression2 if it's not needed.

Just use the ampersand symbol to AND two conditions together. For example, if you wanted to specify the condition 1<x<3, enter it as (x>1)&(x<3).



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