Textbook Question
Graph each function. See Examples 6–8. h(x) = 2x² - 1
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 69
Use a number line to determine whether each statement is true or false. -4 > -3
Verified step by step guidance1
Recall that on a number line, numbers increase in value as you move from left to right.
Identify the positions of -4 and -3 on the number line: -4 is to the left of -3 because -4 is less than -3.
Understand that the inequality -4 > -3 means '-4 is greater than -3', which would imply -4 is to the right of -3 on the number line.
Since -4 is actually to the left of -3, the statement -4 > -3 is false.
Therefore, by comparing their positions on the number line, conclude that the inequality -4 > -3 does not hold true.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Number Line and Ordering of Real Numbers
A number line visually represents real numbers in increasing order from left to right. Numbers to the right are greater than those to the left. Understanding this helps compare negative numbers by their position on the line.
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3:31
Introduction to Complex Numbers
Comparison of Negative Numbers
Among negative numbers, the one with the smaller absolute value is greater. For example, -3 is greater than -4 because -3 is closer to zero on the number line.
Recommended video:
5:02Multiplying Complex Numbers
Inequality Symbols and Their Meaning
The symbol '>' means 'greater than.' When comparing two numbers, 'a > b' means 'a' lies to the right of 'b' on the number line. Correct interpretation of these symbols is essential for evaluating true or false statements.
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5:10Finding the Domain and Range of a Graph
Related Practice
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Simplify each radical. See Example 5. √24
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Factor each polynomial completely. See Example 6. x² - 2x - 15
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
Simplify each complex fraction. See Examples 5 and 6. (−4/3) ÷ (2/9)
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