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Transformation Of Graph Dse Exercise

Mastering the Transformation of Graphs: A Complete DSE Exercise Blueprint

Introduction: Why Graph Transformations Matter in DSE

In the Hong Kong DSE Mathematics examination, the ability to manipulate and interpret graphs is not merely a mechanistic skill—it is a visual language. Questions involving transformation of graphs appear consistently across Papers 1 (Conventional) and 2 (MCQ), as well as in the M2 Calculus paper.

Solution

(a) ( y = f(x) + 3 )
(b) ( y = f(x - 2) )
(c) ( y = f(x + 1) - 4 ) transformation of graph dse exercise

DSE exercises typically categorize transformations into four primary movements: Graph Transformations | Graphs | Maths | FuseSchool Mastering the Transformation of Graphs: A Complete DSE

This report provides:

Solution:
Rewrite as ( y = 3\cos[2(x - \frac\pi2)] + 1 )
Sequence from ( \cos x ): (y = f(2x)) → horizontal compression (graph becomes

  • Further explore other graph transformation techniques, such as graph rewriting and graph composition.
  • Apply graph transformation techniques to real-world problems, such as network optimization and software refactoring.
  • Investigate the use of graph transformation in machine learning and artificial intelligence.
  • (y = f(2x)) → horizontal compression (graph becomes narrower).
  • (y = f(x/2)) → horizontal stretch (graph becomes wider).

Multiple-Choice Identification: You may be given a graph and asked to identify which function ( ) represents it. A common trick is checking the -intercept ( ) or specific vertices.

Worked examples

  1. y = 2f(x) doubles y-values.
  2. y = f(3x) compresses horizontally by factor 1/3.
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