Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 13

Chapter 3, Problem 13

Determine whether each relation defines a function. {(2,4),(0,2),(2,6)}

Verified step by step guidance

Recall that a relation defines a function if every input (x-value) corresponds to exactly one output (y-value).

List the given ordered pairs: (2,4), (0,2), and (2,6).

Identify the input values (x-values) from each pair: 2, 0, and 2.

Check if any input value is repeated with different output values. Here, the input 2 corresponds to both 4 and 6.

Since the input 2 has two different outputs, the relation does not define a function.

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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) is paired with exactly one output (or range element). This means no input value can correspond to more than one output value. Understanding this definition is essential to determine if a given set of ordered pairs represents a function.

Relation as a Set of Ordered Pairs

A relation is a collection of ordered pairs, where the first element is from the domain and the second from the range. Analyzing these pairs helps identify patterns or violations of function rules. Recognizing how to interpret and examine these pairs is key to solving the problem.

Testing for Function Using Input Values

To test if a relation is a function, check if any input value repeats with different outputs. If an input appears more than once with different outputs, the relation is not a function. This step-by-step verification is crucial for answering the question accurately.

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