### Graphing Inequalities

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To create a question using an inequality, we will use the "Area" function. See at the bottom of the function selectors: If you are not sure how to get here, then please first read the page on general Graph authoring.

In order to create a graphing object question such as:

Shade the area inside the circle x2 + y2 = 1 , which is equivalent to :  x2 + y2 <= 1

First create the circle: Use the two points to form the circle, first the center, then any point on the edge. (Read more about conic graphs)

The answer needs to be identified by selecting area mode and click any point inside the circle. In this case, I selected a point close to (0.5,0.5).

Lastly, use "DASHED" to turn the circle edge into the "less than". Note that dashed means not equal to, while solid is equal to. In this example above, we consider the case of less than equal to, but if it is desired to have strictly less than, e.g. x2 + y2 < 1

then use the "Dashed" option like this: We can check the evaluation of this question by click in on "Preview mode" and then "CHECK ANSWER": Here a point was selected outside the circle which is the incorrect location for the inequality and "CHECK ANSWER" shows the graph in red and a score of (0/1).

Here is the correct response: You can make questions with multiple shapes like the following: Here is a more complicated example:

x2/16 - y2/9 <= 1

and

y >2 You can also combine inequalities by the function mode fx and objects such as circles: Or more complicated equations, e.g.  You can also use background images and shapes that will be ignored in the grading: 