MathematicsChapter 1: Functions and Graphs
Stretching and Compressing Graphs
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
Learning objectives
- State the rule for stretching and compressing graphs.
- Solve a stretching and compressing graphs problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
Mathematical form
y=2x2 is vertically stretched
y=(2x)2 is horizontally compressed.
Where / symbols
- Stretching and compressing graphs
- Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
CONCEPT AND RULE
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
METHOD
For stretching and compressing graphs, 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
y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
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 stretching and compressing graphs
- 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:
- y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
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
- Stretching and compressing graphs
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Stretching and Compressing Graphs
Sticky Notes · Formula and Worked Revision
Core Idea
- Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
Rule / Formula
- Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
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
- Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
- Worked pattern: y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
- Final check: domain, sign, notation, units, and reasonableness.
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