Grapher allows you to set many default options, such as the color of a line for a line/scatter plot, the columns used to create plots, and the default font face and size. If you have set these options using the File | Options or File | Defaults commands and the options are not saved, it could be a lack of administrator rights. Default options are saved in two locations in Grapher: in the registry and in the AppData directory. You may need to log into Windows with additional rights to save this information to these locations.
If you are not an administrator, you can resolve this by running the program with administrator rights. To do this, right-click on the Grapher icon or the grapher.exe file, and select Run as administrator. You will be prompted for the administrator password, if needed. Click the File | Defaults command. Make any default changes and click OK. Click the File | Options command. Make any option changes and click OK. Close Grapher. The next time Grapher is opened, the new defaults will be used.