MathematicsChapter 1: Functions and Graphs
Functions, Domain, and Range
A function assigns exactly one output to each input in its domain.
Learning objectives
- 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.
Definition
A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
Where / symbols
- Functions, domain, and range
- 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
- 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.
Worked example
- Worked example:
- For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Functions, domain, and range
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Functions, Domain, and Range
Sticky Notes · Formula and Worked Revision
Core Idea
- A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
Rule / Formula
- A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For f(x)=sqrt(x-2), domain is x>=2 and range is y>=0.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- 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.
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