Textbook Question
Graph each function. See Examples 1 and 2. h(x) = |-½ x|
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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 25
Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.
Verified step by step guidance1
Understand the definition of a function: A relation is a function if every input (or domain value) corresponds to exactly one output (or range value). This means no input is paired with more than one output.
Identify the domain: List all the input values from the given relation. The domain is the set of all these input values.
Identify the range: List all the output values from the given relation. The range is the set of all these output values.
Check if the relation is a function by verifying that each input in the domain maps to only one output in the range. If any input corresponds to multiple outputs, the relation is not a function.
Summarize your findings by stating whether the relation is a function, and clearly write down the domain and range sets using set notation, for example, \(\{x_1, x_2, \ldots\}\) for domain and \(\{y_1, y_2, \ldots\}\) for range.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of a Function
A function is a relation where each input (domain element) corresponds to exactly one output (range element). This means no input value can be paired with more than one output value. Understanding this helps determine if a given relation qualifies as a function.
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Graphs of Common Functions
Domain of a Relation
The domain is the set of all possible input values for the relation. Identifying the domain involves listing or describing all the first elements in the ordered pairs or inputs for which the relation is defined.
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Range of a Relation
The range is the set of all possible output values that the relation can produce. It consists of all second elements in the ordered pairs or outputs corresponding to the domain values.
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5:20Introduction to Relations and Functions
Related Practice
Textbook Question
Graph each function. See Examples 1 and 2. ƒ(x) = -3|x|
Textbook Question
Find each sum or difference. See Example 1. 8 - (-13)
Textbook Question
Solve each linear equation. See Examples 1–3.
5/6x - 2x + 4/3 = 5/3
Textbook Question
Find each sum or difference. See Example 1. -12.31 - (-2.13)
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Textbook Question
Concept Check Let A = {1, 2, 3, 4, 5, 6}, B = {1, 3, 5,}, C = {1, 6}, and D = {4}. Find each set. a. A ∩ D b. B ∩ C c. B ∩ A d. C ∩ A