Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Two-Variable Equations

College Algebra

2. Graphs of Equations

Two-Variable Equations

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1:29 minutes

Problem 23

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Verified step by step guidance

insert step 1: Understand the definition of a function. A relation is a function if each input (x-value) is associated with exactly one output (y-value).

insert step 2: Identify the set of ordered pairs or the mapping diagram provided in the problem.

insert step 3: Check each input value to see if it corresponds to exactly one output value. If any input is associated with more than one output, the relation is not a function.

insert step 4: Determine the domain of the relation, which is the set of all possible input values (x-values).

insert step 5: Determine the range of the relation, which is the set of all possible output values (y-values).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Definition

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 domain, there must be one and only one corresponding y-value. Understanding this definition is crucial for determining whether a given relation qualifies as a function.

Domain and Range

The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Identifying the domain and range helps in understanding the behavior of the function and its limitations. It is essential to analyze the relation to accurately determine these sets.

Vertical Line Test

The vertical line test is a visual method used to determine if a relation is a function. If a vertical line drawn through the graph of the relation intersects it at more than one point, the relation is not a function. This test provides a quick way to assess the function property of a relation graphically.