QuickMath

# Graph Inequalities help

The inequality plot command will generate a plot of almost any inequality in two variables found in high school and undergraduate college mathematics. It will produce plots of single inequalities, or up to eight inequalities on the one graph. Overlapping regions can be easily spotted from their darker shading, and there is even an option for showing just the intersection of all the regions.

To use the inequality plot command, simply go to the basic plot page, type in your inequality (in terms of x and y), enter the set of x and y values for which the plot should be made and hit the "Plot" button. The region satisfied by the inequality will be automatically plotted and the reply will be shown in your browser within a few seconds. If you would like more control over the plotting process, the advanced plot page allows you to overlay several regions in the one diagram as well as to fine-tune the appearance of the plots with a number of options.

Tick marks

Values : checked or unchecked
Default : checked

When Tick marks is checked, the axes on the plot will show tick marks and numerical scales.

Grid lines

Values : checked or unchecked
Default : unchecked

When Grid lines is checked, a blue grid will be superimposed on the graph.

Axes

Values : None or Automatic origin or Origin at (#,#)
Default : Automatic origin

The Axes option controls the appearance and location of the axes on the plot. When None is checked, no axes will be shown at all. When Automatic origin is checked, axes will be shown. The two axes will usually intersect at (0,0), but sometimes this point of intersection will be located elsewhere. When Origin at (#,#) is checked and a point is entered, the axes will be shown and their point of intersection will be forced to be at the specified point.

Aspect ratio

Values : One to one or Golden ratio or # : #
Default : One to one

The Aspect ratio option controls the ratio of the height of the plot to its width. When One to one is checked the ratio is 1:1 and the scales on the two axes will be identical. This will ensure that circles, for example, will actually appear circular on the screen. When Golden ratio is selected, the aspect ratio is 1 : 1/g, where g is the Golden Ratio (approximately 1.6180). This supposedly gives a ratio of height to width which is especially 'pleasing' to the eye. When # : # is selected and two values are entered, the specified aspect ratio will be applied. This is useful if the plot is highly compressed in one direction or the other and needs to be 'stretched-out' to make it clearer.

Display

Values : Intersection of regions or Union of regions
Default : Intersection of regions

The Display option controls how multiple regions are plotted. When Intersection of regions is selected, only those points in the plane which satisfy every single inequality will be shaded. All other points will be shown as white. If there are no points where all the regions intersect, then no shading will be shown at all. When Union of regions is selected, only those points in the plane which satisfy at least one inequality will be shaded. All other points will be shown as white.

Show individual plots

Values : checked or unchecked
Default : checked

When Show individual plots is checked, a separate plot will be generated for each inequality before they are all combined in the final plot on the reply page.