/*! 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 6 Draw the following intervals on ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 6

Draw the following intervals on the number line. $$ (4, \infty) $$

Short Answer

Expert verified
Draw an open circle at 4 and extend a line to the right.

Step by step solution

01

- Understand the Interval Notation

The interval \( (4, \infty) \) denotes all the numbers greater than 4 but does not include 4. \( \infty \) signifies that there is no upper bound.
02

- Identify Key Points on the Number Line

Locate the number 4 on the number line. Since 4 is not included in the interval, you will use an open circle to represent 4.
03

- Draw the Interval

Starting from the open circle at 4, draw a line extending to the right without any end. This indicates all the numbers greater than 4 are included in the interval.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number line
The number line is a visual representation of all numbers in a continuous manner. It helps to easily understand and work with numbers and intervals.
Picture the number line as a straight horizontal line that extends infinitely in both directions. The left side usually represents negative numbers while the right side represents positive numbers.

On the number line, each point corresponds to a unique number. For example, placing an open circle at 4 means that 4 is acknowledged but not included. This becomes very useful when we are asked to draw intervals.
open interval
An open interval includes all the numbers between two endpoints but does not include the endpoints themselves.
For instance, the interval \( (4, \infty) \) starts just after 4 and goes towards infinity, including every number greater than 4.

In such cases, on the number line, we use an open circle to indicate that the endpoint is excluded. The absence of a shaded or filled circle at 4 tells us not to include 4 in our interval. As mentioned before, it indeed visually shows all numbers greater than 4 without any limit, by drawing a continuous line extending to the right.
infinity
Infinity \( (\infty) \) represents a concept of an unbounded quantity. It is not a number but rather an idea of something that goes on endlessly.
In interval notation, infinity is used to show that there is no cap or highest number included.

In our exercise interval \( (4, \infty) \), we use \( \infty \) to indicate that the numbers extend infinitely beyond 4. You can imagine it as a direction rather than a specific point on the number line.
So, as we draw our interval extending continuously to the right from 4, we signify it goes on forever.

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

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \((-3 x)^{3}\)

Evaluate \(f(4)\). \(f(x)=x^{-1}\)

A college student earns income by typing term papers on a computer, which she leases (along with a printer). The student charges $$\$ 4$$ per page for her work, and she estimates that her monthly cost when typing \(x\) pages is \(C(x)=.10 x+75\) dollars. (a) What is the student's profit if she types 100 pages in 1 month? (b) Determine the change in profit when the typing business rises from 100 to 101 pages per month.

In Exercises \(55-58\), find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. $$ f(x)=x^{3}-22 x^{2}+17 x+19 $$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\frac{1}{x^{-3}}\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.