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Functions, Domain, and Range
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
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Functions, Domain, and Range
What is it?
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
In simple words
- A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
- Worked pattern: For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Functions, domain, and range: A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
What you should learn
- State the rule for functions, domain, and range.
- Solve a functions, domain, and range problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
CONCEPT AND RULE
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
METHOD
For functions, domain, and range, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve functions, domain, and range
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Functions, domain, and range
- rule
- worked example
- worked example
How the ideas connect
Worked example: For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
Deeper understanding
Go beyond memorising Functions, Domain, and Range. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Functions, domain, and range
- rule
- worked example
- Functions, domain, and range: A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; r
- CONCEPT AND RULE: A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; r
- METHOD: For functions, domain, and range, identify the given information and required result. Select the mat
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Functions, Domain, and Range: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Functions, domain, and range
- rule
- worked example
- Functions, domain, and range: A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; r
Important formulas
- Functions, domain, and range
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Functions, domain, and range
rule
worked example
Functions, domain, and range: A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; r
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
- Definition
- A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Functions, Domain, and Range.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Functions, Domain, and Range and say why it fits.
Mistake
Q4. State one common mistake students make about Functions, Domain, and Range.
Exam note
Q5. Write a short exam note on Functions, Domain, and Range: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.