In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 3)

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Identify the interval given: \((-\infty, 3)\), which includes all real numbers less than 3 but does not include 3 itself.

Recall that in set-builder notation, we describe the set of all elements \(x\) that satisfy a certain condition.

Since the interval includes all numbers less than 3, write the condition as \(x < 3\).

Express the interval in set-builder notation as \(\{ x \mid x < 3 \}\), which reads as "the set of all \(x\) such that \(x\) is less than 3."

To graph this on a number line, draw a line, mark the point 3 with an open circle (indicating 3 is not included), and shade all points to the left of 3 extending towards negative infinity.

비슷한 문제에 대한 검증된 영상 답변:

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, (-∞, 3) includes all real numbers less than 3 but does not include 3 itself, indicated by the parenthesis. It is a concise way to describe continuous ranges on the number line.

Set-Builder Notation

Set-builder notation describes a set by specifying a property that its members satisfy. For the interval (-∞, 3), it can be written as {x | x < 3}, meaning the set of all x such that x is less than 3. This notation emphasizes the condition defining the set.

Graphing Intervals on a Number Line

Graphing intervals involves shading the portion of the number line that represents the set. For (-∞, 3), the line is shaded to the left of 3, with an open circle at 3 to show it is not included. This visual helps understand the range of values in the interval.