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Translations and Reflections
Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
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Translations and Reflections
What is it?
Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
In simple words
- Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
- Worked pattern: The graph y=-sqrt(x) reflects y=sqrt(x) in the x-axis.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Translations and reflections: Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
What you should learn
- State the rule for translations and reflections.
- Solve a translations and reflections problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
CONCEPT AND RULE
Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
METHOD
For translations and reflections, 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
The graph y=-sqrt(x) reflects y=sqrt(x) in the x-axis.
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 translations and reflections
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
- Translations and reflections
- rule
- worked example
- worked example
How the ideas connect
Worked example: The graph y=-sqrt(x) reflects y=sqrt(x) in the x-axis.
Deeper understanding
Go beyond memorising Translations and Reflections. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: The graph y=-sqrt(x) reflects y=sqrt(x) in the x-axis.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Translations and reflections
- rule
- worked example
- Translations and reflections: Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
- CONCEPT AND RULE: Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
- METHOD: For translations and reflections, identify the given information and required result. Select the mat
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 Translations and Reflections: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Translations and reflections
- rule
- worked example
- Translations and reflections: Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
Important formulas
- Translations and reflections
- 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.
Translations and reflections
rule
worked example
Translations and reflections: Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
- Definition
- Replacing x by x-h shifts right; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
- 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 Translations and Reflections.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Translations and Reflections and say why it fits.
Mistake
Q4. State one common mistake students make about Translations and Reflections.
Exam note
Q5. Write a short exam note on Translations and Reflections: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.