Math Problem Statement
Express the interval in set-builder notation and graph the interval on a number line. (-4,-1)
Solution
The given interval is an open interval, which means that the endpoints and are not included.
Set-builder notation:
In set-builder notation, we express the interval as: This means that is a real number such that is greater than and less than .
Number line graph:
On the number line, the interval is represented by a line segment between and , with open circles at and to indicate that these points are not included in the interval.
I can graph this for you if needed. Would you like to see a visual representation of this?
Here are 5 related questions to expand on:
- How is a closed interval different from an open interval in set-builder notation?
- Can you convert a half-open interval into set-builder notation?
- How do you express the union of two intervals in set-builder notation?
- How would the graph look if the interval was ?
- How do you express inequalities in set-builder notation?
Tip: In set-builder notation, remember to clearly specify the domain and the condition on the variable (e.g., ).
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Math Problem Analysis
Mathematical Concepts
Set Theory
Intervals
Real Numbers
Formulas
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Theorems
Set-builder notation
Suitable Grade Level
Grades 9-12