Transformation Of Graph Dse Exercise < TRUSTED – 2026 >
) by tweaking its equation. For DSE Maths, you mainly need to master these four moves: 1. Translations (Shifts) These slide the graph without changing its shape. Vertical Shift: positive k negative k Horizontal Shift: negative h units (counter-intuitive!). positive h 2. Reflections (Flips) These create a mirror image. Across x-axis: -values change sign; the graph flips upside down). Across y-axis: -values change sign; the graph flips left-to-right). 3. Dilatations (Scaling) These stretch or compress the graph. : Stretch vertically. : Compress vertically. Horizontal: : Compress horizontally (it gets "thinner"). : Stretch horizontally (it gets "wider"). 4. DSE Strategy: The "Order of Operations" If an exercise asks for multiple transformations (e.g., ), follow this order to avoid mistakes: orizontal translation ilatation/Reflection ertical translation
The graph of ( y = f(2x) ) compared to ( y = f(x) ) is: a) Stretched horizontally b) Compressed horizontally c) Stretched vertically d) Shifted right transformation of graph dse exercise
through translation, reflection, and dilation (enlargement/contraction). ) by tweaking its equation
| New equation | Meaning | |--------------|---------| | (y = f(x-a) + b) | Right a, up b | | (y = -f(x)) | Reflect in x-axis | | (y = f(-x)) | Reflect in y-axis | | (y = k f(x)) | Vertical stretch (k>1) / compress (0<k<1) | | (y = f(ax)) | Horizontal compress (a>1) / stretch (0<a<1) | | (y = f(ax + b)) | First factor: (a(x + b/a)) → compress by (1/a), then shift left (b/a) | Vertical Shift: positive k negative k Horizontal Shift:
A helpful trick for DSE students is the "Inside/Outside" distinction: Outside the bracket ): The change is and follows logic ( is a stretch). Inside the bracket ): The change is horizontal and usually works negative h is a compression). Common DSE Pitfalls
