Question
Graph the set \( \{x \mid-1
Ask by Bryant Hammond. in the United States
Feb 24,2025
Ask by Bryant Hammond. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The set \( \{x \mid -1 < x \leq 3\} \) is represented on the number line with an open circle at \(-1\) and a solid circle at \(3\), connected by a line. In interval notation, it is written as \((-1, 3]\).
Solution
Let's solve the problem step by step.
1. **Graphing the Set on the Number Line:**
- The set \( \{x \mid -1 < x \leq 3\} \) includes all numbers greater than \(-1\) and up to and including \(3\).
- On a number line, we represent this as:
- An open circle at \(-1\) (indicating that \(-1\) is not included).
- A solid circle at \(3\) (indicating that \(3\) is included).
- A line connecting these two points, extending to the right from \(-1\) to \(3\).
2. **Writing the Set in Interval Notation:**
- The interval notation for the set \( \{x \mid -1 < x \leq 3\} \) is:
\[
(-1, 3]
\]
Thus, the final answers are:
- The graph on the number line includes an open circle at \(-1\), a solid circle at \(3\), and a line connecting them.
- The interval notation is \((-1, 3]\).
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Simplify this solution Mind Expander
To graph the set \( \{x \mid -1 < x \leq 3\} \) on the number line, you would draw a line with a circle (not filled in) at -1 to indicate that -1 is not included in the set, and a filled circle at 3 to show that 3 is included. Then, shade all the region between these two points, indicating that all numbers greater than -1 and up to 3 are part of the set. In interval notation, this set is represented as \( (-1, 3] \).
