Textbook Question
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 7
In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(-3, -3), (-2, −2), (−1, −1), (0, 0)}
Verified step by step guidance1
Recall that a relation is a function if every input (x-value) corresponds to exactly one output (y-value).
Examine the given set of ordered pairs: \(\{(-3, -3), (-2, -2), (-1, -1), (0, 0)\}\). Check if any x-values repeat with different y-values.
Since all x-values (-3, -2, -1, 0) are unique and each maps to exactly one y-value, this relation is a function.
To find the domain, list all the x-values from the ordered pairs: \(\{-3, -2, -1, 0\}\).
To find the range, list all the y-values from the ordered pairs: \(\{-3, -2, -1, 0\}\).
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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 (or domain element) corresponds to exactly one output (or range element). This means no two ordered pairs can have the same first element with different second elements. Understanding this helps determine if a given set of ordered pairs is a function.
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Domain of a Relation
The domain is the set of all possible input values (first elements) in a relation. Identifying the domain involves listing all unique x-values from the ordered pairs. This is essential for understanding the scope of the relation.
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Range of a Relation
The range is the set of all possible output values (second elements) in a relation. To find the range, list all unique y-values from the ordered pairs. Knowing the range helps describe the outputs the relation can produce.
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Related Practice
Textbook Question
In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(1, 4), (1, 5), (1, 6)}
Textbook Question
Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 3/(x-4) and g(x) = (3/x) + 4
Textbook Question
Find the domain of each function. g(x) = 3/(x2-2x-15)
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Textbook Question
Evaluate each function at the given values of the independent variable and simplify. g(x) = 3x^2 - 5x + 2 (a) g(0), (b) g(-2), (c) g(x-1), (d) g(-x)
Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = f(-x)
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