MAPPING

Mapping

Definition Of Mapping

The idea of pairing each member of the domain with each member of the range referred to as mapping.

Examples of Mapping

The figure shows a mapping of the elements of the domain to the elements of the range. Each element in the domain is increased by 1 to get the corresponding element in the range.

example of Mapping

Video Examples: JEE Math-Mapping

Solved Example on Mapping

Ques: Use the mapping diagram for the relation and determine whether {(3, - 1), (6, - 1),(3, - 2),(6, - 2)} is a function or not.

Choices:

A. Yes
B. No
Correct Answer: B

Solution:

Step 1: Draw the mapping diagram for the given relation.
example of Mapping
Step 2: A relation is a function if each element in the domain is paired with one and only one element in the range.
Step 3: From the mapping diagram, it can be observed that the given relation is not a function as '3' in the domain is paired with two elements - 1 and - 2 in the range and '6' is paired with - 1 and - 2.

Quick Summary

Mapping pairs elements from the domain to the range.
Each element in the domain is associated with one or more elements in the range.

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⚠️ Common Mistakes

Assuming every relation is a function.
Incorrectly identifying the domain and range.

🌍 Real-World Uses

Assigning IP addresses to devices on a network: Each device (domain) is mapped to a unique IP address (range).
Encoding and decoding messages: A character (domain) is mapped to a specific code (range) and vice versa.
Converting Celsius to Fahrenheit: A temperature in Celsius (domain) is mapped to its equivalent in Fahrenheit (range) using a specific function.

🍎 Teacher Insights

Use visual diagrams to illustrate mappings between sets. Emphasize the one-to-one and many-to-one relationships.

🎓 Prerequisites

Sets
Domain
Range
Relations

Check Your Knowledge

Q1: Which of the following best describes a mapping?

A. A set of ordered pairs where each element in the domain maps to exactly one element in the range. B. A pairing of elements from a domain to a range. C. A one-to-one correspondence between two sets. D. A visual representation of a linear equation.

Frequently Asked Questions

Q: What is the difference between a mapping and a function?
A: A function is a special type of mapping where each element in the domain is paired with exactly one element in the range. A mapping does not have this restriction.

Q: Can an element in the range be mapped to by multiple elements in the domain?
A: Yes, multiple elements in the domain can be mapped to the same element in the range.