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Basic Graph Transformations
In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
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Basic Graph Transformations
What is it?
In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
In simple words
- In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
- Worked pattern: y=(x-3)^2+2 is y=x^2 shifted 3 right and 2 up.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Basic graph transformations: In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
What you should learn
- State the rule for basic graph transformations.
- Solve a basic graph transformations problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
CONCEPT AND RULE
In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
METHOD
For basic graph transformations, 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=(x-3)2+2 is y=x2 shifted 3 right and 2 up.
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 basic graph transformations
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
- Basic graph transformations
- rule
- worked example
- worked example
How the ideas connect
Worked example: y=(x-3)^2+2 is y=x^2 shifted 3 right and 2 up.
Deeper understanding
Go beyond memorising Basic Graph Transformations. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: y=(x-3)^2+2 is y=x^2 shifted 3 right and 2 up.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Basic graph transformations
- rule
- worked example
- Basic graph transformations: In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
- CONCEPT AND RULE: In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
- METHOD: For basic graph transformations, identify the given information and required result. Select the matc
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 Basic Graph Transformations: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Basic graph transformations
- rule
- worked example
- Basic graph transformations: In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
Important formulas
- Basic graph transformations
- 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.
Basic graph transformations
rule
worked example
Basic graph transformations: In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
- Definition
- In y=a f(b(x-h))+k, h and k shift the graph; a and b control stretch and reflection.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Basic Graph Transformations.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Basic Graph Transformations and say why it fits.
Mistake
Q4. State one common mistake students make about Basic Graph Transformations.
Exam note
Q5. Write a short exam note on Basic Graph Transformations: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.