Textbook Question
Determine the largest open intervals of the domain over which each function is (c) constant. See Example 8.
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 71
Use a number line to determine whether each statement is true or false. 3 > -2
Verified step by step guidance1
Understand the inequality: The statement is comparing two numbers, 3 and -2, to see if 3 is greater than -2.
Recall the number line concept: On a number line, numbers increase in value as you move from left to right. Negative numbers are to the left of zero, and positive numbers are to the right.
Locate the numbers on the number line: Place -2 to the left of zero and 3 to the right of zero.
Compare their positions: Since 3 is to the right of -2 on the number line, it means 3 is greater than -2.
Conclude the truth value: Based on the number line, the statement 3 > -2 is true.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Number Line Representation
A number line is a visual tool that displays numbers in order from left to right, with smaller numbers on the left and larger numbers on the right. It helps compare values by their positions, making it easier to determine which number is greater or smaller.
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Introduction to Complex Numbers
Inequality Symbols and Meaning
The symbol '>' means 'greater than,' indicating that the number on the left side is larger than the number on the right side. Understanding this helps interpret and verify statements comparing two numbers.
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5:10Finding the Domain and Range of a Graph
Comparing Positive and Negative Numbers
Positive numbers are always greater than negative numbers because they lie to the right of zero on the number line. Recognizing this helps quickly determine the truth of inequalities involving positive and negative values.
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Guided course
05:50Drawing Angles in Standard Position
Related Practice
Textbook Question
Simplify each complex fraction. See Examples 5 and 6. (y/r) ÷ (x/y)
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Textbook Question
Graph each function. See Examples 6–8. ƒ(x) = 2(x - 2)² - 4
Textbook Question
Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.
Textbook Question
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).
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Textbook Question
Determine the largest open intervals of the domain over which each function is (b) decreasing. See Example 8.
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