/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Express each interval in set-bui... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 14

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 3.5]$$

Short Answer

Expert verified
The set-builder notation for the interval \( (-\infty, 3.5] \) is \( \{ x : x \in \mathbb{R}, x \leq 3.5 \} \). A graph of this interval on a number line would include a solid circle at 3.5, with an arrow pointing leftwards, towards negative infinity.

Step by step solution

01

Understanding the Interval Notation

Consider the interval given as \( (-\infty, 3.5] \). The parenthesis '(' denotes that the interval starts from negative infinity and does not include any real number i.e., the interval is open towards negative infinity. The square bracket ']' indicates that the interval ends at 3.5 and includes the number 3.5 i.e., the interval is closed at 3.5.
02

Converting to Set-builder Notation

Set-builder notation provides a precise method to describe sets. The interval notation can be translated into set builder notation as: \( S = \{ x : x \in \mathbb{R}, x \leq 3.5 \} \). Meaning, S is the set of all x such that x is a real number and x is less than or equal to 3.5.
03

Graphing the Interval on a Number Line

To graph the interval on a number line, start with a straight horizontal line. This represents the number line. Draw a filled circle at the point corresponding to the number 3.5, as it is included in the interval. Draw an arrow pointing to the left starting from the filled circle to represent all numbers less than 3.5. The arrow continues indefinitely to represent the negative infinity.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How is the quadratic formula derived?

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=2 k w+ \quad 2 l h+ \quad 2 w h \text { for } h$$

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y_{1}=x-3, y_{2}=x+8, \text { and } y_{1} y_{2}=-30 $$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=lw \quad \text{for} \quad w$$

You invested \(\$ 11.000\) in two accounts paying \(5 \%\) and \(8 \%\) annual interest. If the total interest earned for the year was \(\$ 730,\) how much was invested at each rate?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.