Math Problem Statement

The number line shows an interval from -1 to 4, with an open interval at -1 and a closed interval at 4. What is the interval notation?

Solution

The image you provided shows a number line representing an interval, which is a segment of the real number line. The segment appears to start at 1-1 and ends at 44, and it includes these key characteristics:

  • The line segment starts at 1-1 and extends to 44.
  • The bracket on 44 is square (closed interval), meaning that 44 is included in the interval.
  • The parentheses at 1-1 are rounded (open interval), indicating that 1-1 is not included in the interval.

Based on this, the interval can be written in interval notation as: (1,4](-1, 4]

This represents all numbers greater than 1-1 and less than or equal to 44.

Would you like further explanation or have any questions? Here are five questions related to this concept:

  1. How do you represent an open interval and a closed interval in set notation?
  2. What is the difference between an open and a closed interval?
  3. How would you graph the interval [1,5)[1, 5) on a number line?
  4. Can a number line represent multiple intervals at once?
  5. How can intervals be used to describe the solution sets of inequalities?

Tip: When solving inequalities, always pay attention to whether the boundary values are included (closed intervals) or excluded (open intervals).

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Math Problem Analysis

Mathematical Concepts

Intervals
Number Line
Real Numbers

Formulas

Interval notation (a, b], [a, b)
Open and closed intervals

Theorems

The concept of intervals in real number theory
Set theory for open and closed sets

Suitable Grade Level

Grades 6-8