Math Problem Statement

Which of the following diagrams shows the shaded region -2 < y ≤ 3?

Solution

The inequality given is 2<y3-2 < y \leq 3, which describes a vertical strip on the coordinate plane.

  • The yy-values range from slightly greater than 2-2 to 33. This means the shaded region should lie between the lines y=2y = -2 (dotted line since yy is not equal to 2-2) and y=3y = 3 (solid line since yy is less than or equal to 33).

Looking at the diagrams:

  • Diagram B is the correct answer. It shows a vertical strip where yy ranges from 2-2 (dotted line) to 33 (solid line), consistent with the inequality 2<y3-2 < y \leq 3.

Would you like more details on why Diagram B matches the inequality?

Here are 5 related questions to expand on this:

  1. How do you graph inequalities involving both upper and lower bounds like 2<y3-2 < y \leq 3?
  2. What is the significance of using dotted versus solid lines in graphing inequalities?
  3. How would you represent the inequality 3y<2-3 \leq y < 2 on a graph?
  4. How can inequalities involving xx instead of yy be represented graphically?
  5. What changes if the inequality were 2y3-2 \leq y \leq 3 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