Math Problem Statement
Choose the correct interval notation for the graph. (You get only one try for the answer; be careful.)
Interval Notation
(-∞, -3] ⋃ [3,7)
(-∞, -3) ⋃ (3,7)
[-∞, -3) ⋃ [-3,7]
(-∞, -3) ⋃ [3, 7] None of these
Solution
To determine the correct interval notation for the graph, we need to interpret the notation provided:
- None of these
Here’s a quick review of interval notation:
- : All numbers less than , not including .
- : All numbers less than or equal to , including .
- : All numbers between and , not including or .
- : All numbers between and , including but not .
- : All numbers between and , including both and .
Considering each option:
- includes all numbers less than or equal to and all numbers from to , including but not .
- includes all numbers less than and all numbers from to , not including or .
- is incorrect because is not a proper interval notation.
- includes all numbers less than and all numbers from to , including and .
If we visualize these on a number line, it becomes clearer which intervals include the boundary points:
- If is included (closed interval at ), then we must have .
- If is included (closed interval at ), then we must have .
So, the correct choice based on typical interval conventions would be the one that includes these specific boundaries correctly.
Considering the provided intervals:
- includes and excludes , which might match common graphing conventions.
Therefore, the correct interval notation for the graph is:
(-∞, -3] ⋃ [3,7).
Do you want details or have any questions?
Here are 5 related questions to expand your understanding:
- How do you determine whether to use a square bracket or a parenthesis in interval notation?
- Can you explain the difference between an open interval and a closed interval?
- How would you represent the interval where all numbers between -5 and 5 are included, but not -5 and 5 themselves?
- What is the union of the intervals and ?
- How can interval notation be used to describe the domain of a function?
Tip: Always sketch a number line when working with interval notation to visually confirm which points are included or excluded.
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Math Problem Analysis
Mathematical Concepts
Algebra
Interval Notation
Set Theory
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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