Objects can leave a trace in the [img]https://www.geogebra.org/wiki/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] when they are moved. There are two ways of showing the trace of an object:[br][list][*]Select the object whose trace you would like to show. Use the [img]https://wiki.geogebra.org/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i] button to open the [img]https://wiki.geogebra.org/uploads/thumb/3/30/Menu-options.svg/16px-Menu-options.svg.png[/img] [i]Settings.[/i] Check [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] [i]Show Trace[/i] on tab [i]Basic[/i].[br]OR[/*][*]Right-click (MacOS: [i]Ctrl[/i]-click, tablet: long tap) an object and check [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] [i]Show[/i] [i]Trace[/i] in the appearing context menu. [/*][/list]Then, modify the construction so that the object, whose trace you turned on, changes its position and leaves a trace in the [img]https://www.geogebra.org/wiki/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i].
Graph the derivative of a function [math]f\left(x\right)=\frac{x^2}{2}+1[/math] by tracing the slope of point A.
Move point [i]A[/i] so that the point [i]S[/i] graphs the slope function.
Re-create the construction above by following the steps listed below:[br][table][tr][td][size=100]1.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][br][/td][td][size=100]Enter the polynomial [code][/code][code]f(x) = x^2/2 + 1[/code].[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_pointonobject.png[/icon][br][/td][td][size=100]Create a new point [i]A[/i] on function [i]f[/i].[br][b]Hint:[/b] Point A can only be moved along the function.[/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_tangent.png[/icon][/size][/td][td][size=100]Create tangent [i]g[/i] to function [i]f[/i] through point [i]A[/i].[/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][br][/td][td][size=100]Create the slope of tangent [i]g[/i] using [code]m = Slope(g)[/code].[/size][/td][/tr][tr][td][size=100]5.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][br][/td][td][size=100]Define point [code]S = (x(A), m)[/code].[br][b]Hint:[/b] [code]x(A)[/code] gives you the [i]x[/i]-coordinate of point [i]A[/i].[/size][/td][/tr][tr][td][size=100]6.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/size][/td][td][size=100]Connect points [i]A[/i] and [i]S[/i] using a segment.[/size][/td][/tr][tr][td][size=100]7.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/32px-Menu-trace-on.svg.png[/icon][/td][td][size=100]Turn on the trace of point [i]S [/i]and move point [i]A[/i]. [br][b]Hint: [/b]Right-click point [i]S[/i] (MacOS: Ctrl-click, tablet: long tap) and select [i]Show Trace[/i].[br][/size][/td][/tr][tr][td]8.[/td][td][img]https://www.geogebra.org/wiki/uploads/thumb/f/f6/Menu-button-open-menu.svg/32px-Menu-button-open-menu.svg.png[/img][/td][td]Close the [img]https://www.geogebra.org/wiki/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] by unchecking the corresponding option in the [img]https://www.geogebra.org/wiki/uploads/thumb/6/67/Menu-view.svg/16px-Menu-view.svg.png[/img] [i]View [/i]Menu.[/td][/tr][tr][td]9.[/td][td][img]https://www.geogebra.org/wiki/uploads/thumb/f/f6/Menu-button-open-menu.svg/32px-Menu-button-open-menu.svg.png[/img][/td][td]Display the [i]Input Bar [/i]using the [img]https://www.geogebra.org/wiki/uploads/thumb/6/67/Menu-view.svg/16px-Menu-view.svg.png[/img] [i]View [/i]Menu.[/td][/tr][/table]
Change the equation of the initial polynomial [i]f(x)[/i] to produce a new problem. For example, enter [code]f(x)= 2 x²[br][/code]into the [i]Input Bar[/i]. You might want to zoom if point [i]A [/i]lays outside of the visible area after changing the function.
The [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] [i]Show Trace[/i] feature has some special characteristics:[br][list][*]A trace is a temporary phenomenon. Whenever the graphics are refreshed, the trace disappears (e.g. on zoom). If you want to display a permanent trace of a point you can use the [size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_locus.png[/icon][/size] [url=https://wiki.geogebra.org/en/Locus]Locus[/url] tool or command.[br][/*][*]The trace cannot be saved and is not shown in the [img]https://www.geogebra.org/wiki/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i].[br][/*][*]You can turn off the trace of an object by unchecking [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] [i]Show[/i] [i]Trace[/i] either in the [img]https://wiki.geogebra.org/uploads/thumb/3/30/Menu-options.svg/16px-Menu-options.svg.png[/img] [i]Settings[/i] or the context menu.[br][/*][*]The menu item [i]Refresh Views[/i] in the [img]https://wiki.geogebra.org/uploads/thumb/6/67/Menu-view.svg/16px-Menu-view.svg.png[/img] [i]View[/i] menu clears all traces.[br][b]Hint[/b]: If you are using [i]GeoGebra [/i]Desktop or the Online or Tablet App, you can also use the key combination [i]Ctrl – F[/i] to refresh the [i]Views[/i].[/*][/list]