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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1:37 minutes

Problem 22

Textbook Question

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

Verified step by step guidance

Identify the pairs of values in the relation: (4, 18), (9, 25), (13, 28), (19, 35).

Determine if each input (first element of each pair) maps to exactly one output (second element of each pair).

Since each input value maps to a unique output value, the relation is a function.

List the domain, which consists of all the input values: {4, 9, 13, 19}.

List the range, which consists of all the output values: {18, 25, 28, 35}.

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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 is only one corresponding y-value in the range. To determine if a relation is a function, one can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not 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 is crucial for understanding the behavior of a function. In the given relation, the domain consists of the numbers 4, 9, 13, and 19, while the range includes the outputs 18, 25, 28, and 35.

Mapping Diagrams

Mapping diagrams visually represent the relationship between the domain and range of a function. In these diagrams, arrows indicate how each input is connected to its corresponding output. They help in quickly assessing whether a relation is a function by showing the connections clearly, making it easier to identify if any input is linked to multiple outputs.