AS/A-Level Mathematics - Transformation of graphs

Let's learn about how graphs can be transformed with a little change on the function in A-Level Maths!

Transformation of graphs

The transformations so far follow these rules:  

• f(x) + a is f(x) shifted upward a units 
• f(x) – a is f(x) shifted downward a units 
• f(x + a) is f(x) shifted left a units 
• f(x – a) is f(x) shifted right a units 
• –f(x) is f(x) flipped upside down ("reflected about the x-axis") 
• f(–x) is the mirror of f(x) ("reflected about the y-axis") 

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Drafted by Eunice (Maths)

References:

https://socratic.org/questions/how-do-you-sketch-the-graph-of-y-x-2-2-2-and-describe-the-transformation-1

https://www.pearson.com/uk/educators/schools/subject-area/mathematics/unrivalled-support/support-from-pearson/gcse-maths-transition-to-alevel/chapter-four-graphs-and-transformations.html

https://www.storyofmathematics.com/transformations-of-functions

https://www.tes.com/teaching-resource/transformation-of-graphs-revision-11255756