In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2, ∞)

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Identify the interval given: (2, \(\infty\)). This interval includes all real numbers greater than 2 but does not include 2 itself.

Recall that in set-builder notation, we describe the set of all elements x that satisfy a certain condition. Here, the condition is that x is greater than 2.

Write the set-builder notation as: \(\{ x \mid x > 2 \}\), which reads as "the set of all x such that x is greater than 2."

To graph this interval on a number line, draw a number line and mark the point 2 with an open circle to indicate that 2 is not included in the interval.

Shade the number line to the right of 2 extending towards positive infinity to represent all numbers greater than 2.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Interval Notation

Interval notation is a way to represent a set of numbers between two endpoints. For example, (2, ∞) means all numbers greater than 2 but not including 2, extending to infinity. Parentheses indicate that endpoints are not included, while brackets indicate inclusion.

Set-Builder Notation

Set-builder notation describes a set by specifying a property that its members must satisfy. For intervals, it typically uses a variable and an inequality, such as {x | x > 2}, meaning the set of all x such that x is greater than 2.

Graphing Intervals on a Number Line

Graphing an interval involves shading the portion of the number line that represents the set. Open circles indicate endpoints not included (like 2 in (2, ∞)), and shading extends towards infinity to show all numbers greater than the endpoint.