Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Intro to Functions & Their Graphs
0:50 minutes
Problem 11a
Textbook Question
Textbook QuestionDetermine whether each relation defines a function. See Example 1. {(5,1),(3,2),(4,9),(7,8)}
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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 specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that for every x-value in the set of ordered pairs, there must be a unique y-value. If any x-value corresponds to more than one y-value, the relation cannot be classified as a function.
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Ordered Pairs
Ordered pairs are pairs of elements written in the form (x, y), where x is the first element and y is the second. In the context of relations, these pairs represent the relationship between two sets, typically the domain and range. Analyzing ordered pairs helps determine if a relation meets the criteria to be a function by checking the uniqueness of y-values for each x-value.
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Vertical Line Test
The vertical line test is a visual method used to determine if a graph represents a function. If any vertical line drawn on the graph intersects the curve at more than one point, the relation is not a function. This test reinforces the concept that each input must correspond to a single output, providing a practical way to assess functions graphically.
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