MathematicsChapter 6: Functions and Graphs
Domain and Range
f(x)=sqrt(x) has domain x>=0 and range y>=0.
Learning objectives
- Define and explain domain and range.
- Apply domain and range to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
f(x)=sqrt(x) has domain x>=0 and range y>=0. f(x)=1x has domain x!=0. f(x)=|x| has range y>=0. Read restrictions from the formula before evaluating.
Where / symbols
- Domain And Range
- f(x)=sqrt(x) has domain x>=0 and range y>=0. f(x)=1/x has domain x!=0. f(x)=|x| has range y>=0. Read restrictions from the formula before evaluating.
Relationship
- domain = inputs
Overview
Learn the idea, then use it:
Core Understanding
f(x)=sqrt(x) has domain x>=0 and range y>=0. f(x)=1x has domain x!=0. f(x)=|x| has range y>=0. Read restrictions from the formula before evaluating.
Examples where it is defined · one output per input · domain = inputs · DOMAIN AND RANGE: f(x)=sqrt(x) has domain x>=0 and range y>=0. f(x)=1/x has domain x!=0. f(x)=|x| has range y>=0. Read restrictions from t
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — DOMAIN AND RANGE
f(x)=sqrt(x) has domain x>=0 and range y>=0. f(x)=1x has domain x!=0. f(x)=|x| has range y>=0. Read restrictions from the formula before evaluating.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge domain and range with a neighbouring idea that uses a different definition, rule, or method.
Key points
- where it is defined
- one output per input
- domain = inputs
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Domain and Range
Sticky Notes · Quick Revision
Core Idea
- f(x)=sqrt(x) has domain x>=0 and range y>=0.
Key Points
- where it is defined
- one output per input
- domain = inputs
Simple Check
- Explain domain and range in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge domain and range with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- f(x)=sqrt(x) has domain x>=0 and range y>=0.
- where it is defined
- one output per input
- domain = inputs
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