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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
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 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)}
Guida verificata passo dopo passo1
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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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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Graphs of Common Functions
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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5:20Relations and Functions
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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5:20Relations and Functions
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