Changes made inside the function's argument counter-intuitively affect the -coordinates. The graph moves opposite to the sign. shifts the graph to the left by Horizontal Translation Rightward: shifts the graph to the right by Horizontal Stretching/Compressing: compresses the graph horizontally by a factor of 1k1 over k end-fraction , and stretches it if Reflections Reflections flip the graph across the coordinate axes. Reflection across the x-axis: negates all -values, flipping the graph vertically. Reflection across the y-axis: negates all -values, flipping the graph horizontally. 2. Systematic Workflow for Successive Transformations
This exercise set covers exactly the type of appearing in DSE Paper 1 (short questions) and occasionally Paper 2 (MC). Practice translating between algebraic descriptions, coordinate mappings, and geometric sketches.
Every transformation can be categorized into one of four movements. To succeed, you must distinguish between changes (affecting the output ) and Horizontal changes (affecting the input A. Translation (Shifting) Vertical Shift: +kpositive k moves the graph up ; −knegative k moves it down . Horizontal Shift: Counter-intuitive rule: moves the graph right , while moves it left . B. Reflection (Flipping) Reflection in x-axis: The graph flips upside down (all -coordinates change sign). Reflection in y-axis: The graph flips horizontally (left becomes right). C. Scaling (Enlarging/Compressing) Vertical Stretch/Compression: , the graph stretches vertically. If , it compresses. Horizontal Stretch/Compression: Counter-intuitive rule: If , the graph compresses horizontally by a factor of , it stretches . 2. Common DSE Pitfalls to Avoid The "Opposite" Rule for : Students often forget that operations inside the bracket
Follow the reverse of standard algebraic operations (De-bracketization rule). For , shift horizontally by first, then scale horizontally by . Alternatively, factorize the expression to to scale first, then shift. transformation of graph dse exercise
, the graph (becomes flatter) by a factor of Horizontal Scaling:
This article provides a deep dive into the types of transformations, the rules governing them, and a structured exercise guide designed to help you excel in the DSE Compulsory Part. 1. What is Transformation of Graph DSE Exercise?
When you encounter a graph transformation question in DSE, follow this : Reflection across the x-axis: negates all -values, flipping
This exercise explores the same transformation from different perspectives, a common theme in higher-level DSE questions.
Adding or subtracting a constant outside the function moves the graph vertically. Rule: If , the graph shifts upward by , it shifts downward. Coordinate Change: 2. Horizontal Translation (Shifting Left or Right)
Mastering the Transformation of Graphs for the HKDSE Graph transformation is a core algebraic topic in the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics curriculum. Mastering this topic allows you to score well in both the compulsory Section A and the multiple-choice Section B. the graph shifts upward by
We apply the transformation to each coordinate of point ( P ).
There are four primary types of graph transformations: