Explain how to know wheather the endpoint of the graph of an inequality should be a closed dot or an open dot.
It should be an open dot because it's an inequality. It would be a closed dot if it was an equality, such as x=3.
If the inequality contains either ≤ or ≥, then close the dot of the endpoint, since that point is included in the graph.
If the inequality contains eitehr < or > , then leave the dot open to show that the endpoint itself is not included in your graph.
yes! if it is addition or subtraction you have an open dot! if it multiplication or division than a closed dot!
3
x<−3, would you use a closed dot or an open dot?
To determine whether the endpoint of the graph of an inequality should have a closed dot (●) or an open dot (○), you need to consider two factors: the nature of the inequality and whether the endpoint itself is included in the solution.
1. Determine the nature of the inequality:
- If the inequality is > (greater than) or < (less than), it indicates that the solution should be an open dot (○).
- If the inequality is ≥ (greater than or equal to) or ≤ (less than or equal to), it indicates that the solution should be a closed dot (●).
2. Consider whether the endpoint is included in the solution:
- If the inequality includes the equal sign (≥ or ≤), then the endpoint is included in the solution, indicating a closed dot (●).
- If the inequality does not include the equal sign (> or <), then the endpoint is not included in the solution, indicating an open dot (○).
Let's look at a couple of examples to illustrate these principles:
Example 1: Graphing the inequality x > 3
- The inequality is >, which indicates an open dot (○).
- Since there is no equal sign, the endpoint is not included in the solution, confirming an open dot (○).
Example 2: Graphing the inequality y ≤ -2
- The inequality is ≤, which indicates a closed dot (●).
- Since there is an equal sign, the endpoint is included in the solution, confirming a closed dot (●).
By considering the nature of the inequality and whether the endpoint is included, you can determine whether to use a closed dot (●) or an open dot (○) when graphing the inequality.