Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 30

Chapter 1, Problem 30

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Whole numbers

Verified step by step guidance

Recall the definition of whole numbers: Whole numbers are the set of numbers that include all non-negative integers starting from 0, i.e., \(\{0, 1, 2, 3, \ldots\}\).

Examine each element of the set \(A = \{-6, -\frac{12}{4}, -\frac{5}{8}, -\sqrt{3}, 0, \frac{1}{4}, 1, 2\pi, 3, \sqrt{12}\}\) to determine if it is a whole number.

Check if the element is a non-negative integer (0 or positive integer) without any fractional or irrational part.

Identify the elements that satisfy this condition: 0, 1, 3 (since \(\sqrt{12}\) is not an integer and \(2\pi\) is irrational, and the others are negative or fractions).

List these elements as the subset of \(A\) that are whole numbers: \(\{0, 1, 3\}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Definition of Whole Numbers

Whole numbers are the set of non-negative integers starting from zero, including 0, 1, 2, 3, and so on. They do not include fractions, decimals, negative numbers, or irrational numbers. Understanding this helps identify which elements from a given set qualify as whole numbers.

Number Classification

Number classification involves categorizing numbers into sets such as integers, rational numbers, irrational numbers, and whole numbers. Recognizing the properties of each type allows for accurate sorting of elements based on their characteristics, such as sign, fractional form, or irrationality.

Simplification and Evaluation of Expressions

Simplifying expressions like fractions and radicals is essential to determine their exact value and type. For example, simplifying -12/4 to -3 or √12 to 2√3 helps decide if the number fits into the whole numbers set, which requires the number to be a non-negative integer.

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For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

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Find each sum or difference. See Example 1. 9⁄10 - ( -4⁄3)

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For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = ½ x - 2

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Find each sum or difference. See Example 1. |-8 - 6|

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Graph each function. See Examples 1 and 2. ƒ(x) = -√-x

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Find the square of each radical expression. See Example 2. -√19

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