Math Problem Statement
Sketch the region given by the set \(\{(x, y) \mid |x| \leq 4\}\).
Solution
The problem asks you to sketch the region given by the set .
Steps to solve:
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Understanding the Inequality: The inequality means that the -coordinate of any point in the region must satisfy this condition. Since , this translates to .
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Graphing the Region:
- The inequality represents a vertical strip on the graph where the -values range between and .
- There are no restrictions on the -values, so can take any value.
- Therefore, the region consists of all points between the vertical lines and , inclusive of the boundary.
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Sketching:
- Draw two vertical lines at and .
- Shade the region between these two lines, extending infinitely in the -direction.
This is the graphical representation of the region given by .
Do you want any additional details or have any questions?
Related Questions:
- What is the graphical representation of ?
- How would the region change if the inequality were strict, i.e., ?
- What is the interpretation of in terms of graphing?
- How would you graph the inequality ?
- What does the region look like for the system of inequalities and ?
Tip: When dealing with absolute value inequalities, it is often helpful to break them down into compound inequalities for easier visualization.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Absolute Value
Graphing
Formulas
|x| \leq 4
-4 \leq x \leq 4
Theorems
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Suitable Grade Level
Grades 7-10