How do you know when to use an open or closed circle when graphing inequalities?

An open circle means not equal to. So, if your equation is x < 4, You would put an OPEN circle at four because it can't equal four.

Answered by KBreithaupt | 2024-06-24

When graphing inequalities, the type of circle used indicates whether the boundary point is included in the solution set or not. An open circle is used when graphing strict inequalities, such as y > x or y < x , which do not include the boundary point. Conversely, a closed circle is used for non-strict inequalities indicating that the boundary point is part of the solution set. The independent variable typically goes on the horizontal axis, and the dependent variable on the vertical axis.
While creating the graph, it's essential to choose the correct graph type (line, bar, etc.) based on whether your variables are continuous. Also, using visual cues like dashed lines can help interpret the graph correctly. And remember, the sign of the derivative in a differential equation, indicated by arrows on a directional field graph, shows whether the variable is increasing or decreasing within specific regions of the graph.

Answered by AliciaAugello | 2024-06-24

Use an open circle for inequalities that do not include the endpoint (like < or >) and a closed circle for those that do include the endpoint (like ≤ or ≥). This visually indicates which values are part of the solution set. Properly using circles helps clarify your inequality representations on a number line.
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Answered by KBreithaupt | 2024-12-26