5 min read
Stretching and Compressing Graphs
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
Choose Your Level
Stretching and Compressing Graphs
What is it?
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
In simple words
- 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.
Important terms
Stretching and compressing graphs: Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
What you should learn
- 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.
Recommended for Class 12
Full school-level explanation
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
How it works
- 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.
Remember
- Stretching and compressing graphs
- rule
- worked example
- worked example
How the ideas connect
Worked example: y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
Deeper understanding
Go beyond memorising Stretching and Compressing Graphs. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: y=2x^2 is vertically stretched; y=(2x)^2 is horizontally compressed.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Stretching and compressing graphs
- rule
- worked example
- Stretching and compressing graphs: Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocall
- CONCEPT AND RULE: Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocall
- METHOD: For stretching and compressing graphs, identify the given information and required result. Select th
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Stretching and Compressing Graphs: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Stretching and compressing graphs
- rule
- worked example
- Stretching and compressing graphs: Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocall
Important formulas
- Stretching and compressing graphs
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Stretching and compressing graphs
rule
worked example
Stretching and compressing graphs: Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocall
Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
- Definition
- Multiplying f(x) changes vertical scale; multiplying x inside f changes horizontal scale reciprocally.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
You've completed the learning section.
Exam Practice
Define
Q1. Define Stretching and Compressing Graphs.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Stretching and Compressing Graphs and say why it fits.
Mistake
Q4. State one common mistake students make about Stretching and Compressing Graphs.
Exam note
Q5. Write a short exam note on Stretching and Compressing Graphs: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.