Math Problem Statement
Which of the following diagrams shows the shaded region -2 < y ≤ 3?
Solution
The inequality given is , which describes a vertical strip on the coordinate plane.
- The -values range from slightly greater than to . This means the shaded region should lie between the lines (dotted line since is not equal to ) and (solid line since is less than or equal to ).
Looking at the diagrams:
- Diagram B is the correct answer. It shows a vertical strip where ranges from (dotted line) to (solid line), consistent with the inequality .
Would you like more details on why Diagram B matches the inequality?
Here are 5 related questions to expand on this:
- How do you graph inequalities involving both upper and lower bounds like ?
- What is the significance of using dotted versus solid lines in graphing inequalities?
- How would you represent the inequality on a graph?
- How can inequalities involving instead of be represented graphically?
- What changes if the inequality were instead?
Tip: When graphing inequalities, always check the boundary types (solid or dotted) to represent strict or non-strict inequalities.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Graphing inequalities
Coordinate plane
Formulas
None (graphical representation of inequality)
Theorems
Graphing linear inequalities
Suitable Grade Level
Grades 6-8