MathematicsChapter 1: Functions and Graphs
Graph-Based Modelling
Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
Learning objectives
- State the rule for graph-based modelling.
- Solve a graph-based modelling problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
Where / symbols
- Graph-based modelling
- Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
CONCEPT AND RULE
Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
METHOD
For graph-based modelling, 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 C(n)=500+20n, C(10)=700 and the practical domain has n>=0 whole.
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 graph-based modelling
- 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 C(n)=500+20n, C(10)=700 and the practical domain has n>=0 whole.
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
- Graph-based modelling
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Graph-Based Modelling
Sticky Notes · Formula and Worked Revision
Core Idea
- Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
Rule / Formula
- Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- If C(n)=500+20n, C(10)=700 and the practical domain has n>=0 whole.
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
- Choose variables, fit a suitable function, state units and domain, then interpret rather than merely calculate.
- Worked pattern: If C(n)=500+20n, C(10)=700 and the practical domain has n>=0 whole.
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.