Ch. R - Algebra Review

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

Lial 12th Edition

Ch. R - Algebra Review

Problem 32

Chapter 1, Problem 32

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. Rational numbers

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Recall that rational numbers are numbers that can be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \). This includes integers, fractions, and terminating or repeating decimals.

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 can be written as a fraction of integers.

Identify \( -6 \) as rational because it is an integer, which can be written as \( \frac{-6}{1} \).

Simplify \( -\frac{12}{4} \) to \( -3 \), which is also an integer and therefore rational.

Recognize \( -\frac{5}{8} \), \( 0 \), \( \frac{1}{4} \), \( 1 \), and \( 3 \) as rational numbers since they are either fractions or integers.

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Key Concepts

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

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This includes integers, fractions, and finite or repeating decimals. For example, 1/2, -3, and 0.75 are rational, while numbers like √3 or π are not.

Set Membership and Classification

Understanding set membership involves determining whether an element belongs to a particular set based on its properties. Classifying numbers into sets like rational or irrational requires analyzing their form and characteristics, such as whether they can be expressed as a fraction or not.

Simplification of Expressions

Simplifying expressions, such as fractions or radicals, helps identify the nature of numbers. For example, simplifying -12/4 to -3 or √12 to 2√3 clarifies whether the number is rational or irrational, aiding in accurate classification within sets.

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Simplifying Trig Expressions

Related Practice

Textbook Question

Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x = 5x + 24 + x

Textbook Question

Find the square of each radical expression. See Example 2. √3x² + 4

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Textbook Question

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. Integers

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y = x²

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Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x = y⁶

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Textbook Question

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 = x²

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