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

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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2:02 minutes

Problem 20

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4. {(2,5),(3,7),(3,9),(5,11)}

Verified step by step guidance

Step 1: Understand the definition of a function. A relation is a function if each input (or domain value) is associated with exactly one output (or range value).

Step 2: Examine the given set of ordered pairs: \((2,5), (3,7), (3,9), (5,11)\).

Step 3: Check for repeated input values. Notice that the input value '3' is associated with two different outputs: '7' and '9'.

Step 4: Conclude that the relation does not define a function because the input '3' maps to more than one output.

Step 5: Identify the domain and range. The domain is the set of all input values: \{2, 3, 5\}. The range is the set of all output values: \{5, 7, 9, 11\}.

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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 any given x-value, there cannot be multiple corresponding y-values. Understanding this definition is crucial for determining whether a 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 the values it can take. In the given relation, analyzing the pairs will reveal both the domain and range.

Identifying Non-Function Relations

To determine if a relation is not a function, one must look for instances where a single input is paired with multiple outputs. In the provided relation, the presence of the input '3' associated with both '7' and '9' indicates that it does not define a function. Recognizing these patterns is essential for accurate classification.