MathematicsChapter 1: Functions and Graphs
Function Notation and Evaluation
In f(a), substitute a for every x while preserving brackets and the stated domain.
Learning objectives
- State the rule for function notation and evaluation.
- Solve a function notation and evaluation problem step by step.
- Check the result, restrictions, notation, and units.
Definition
In f(a), substitute a for every x while preserving brackets and the stated domain.
Where / symbols
- Function notation and evaluation
- In f(a), substitute a for every x while preserving brackets and the stated domain.
CONCEPT AND RULE
In f(a), substitute a for every x while preserving brackets and the stated domain.
METHOD
For function notation and evaluation, 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
If f(x)=2x2-3, then f(-2)=2(4)-3=5.
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 function notation and evaluation
- 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:
- If f(x)=2x2-3, then f(-2)=2(4)-3=5.
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
- Function notation and evaluation
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Function Notation and Evaluation
Sticky Notes · Formula and Worked Revision
Core Idea
- In f(a), substitute a for every x while preserving brackets and the stated domain.
Rule / Formula
- In f(a), substitute a for every x while preserving brackets and the stated domain.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- If f(x)=2x2-3, then f(-2)=2(4)-3=5.
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
- In f(a), substitute a for every x while preserving brackets and the stated domain.
- Worked pattern: If f(x)=2x^2-3, then f(-2)=2(4)-3=5.
- Final check: domain, sign, notation, units, and reasonableness.
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