In the HKDSE Mathematics curriculum, Transformation of Graphs is a critical topic frequently appearing in Paper 1 (Section A and B) and Paper 2 (Multiple Choice). It involves changing a parent function
The key to mastering this topic is distinguishing between "Inside" (horizontal) and "Outside" (vertical) changes. Transformation Type Effect on Graph Effect on Coordinates Vertical Translation Move up by Move down by Horizontal Translation Move left by Move right by Vertical Reflection Reflect in x-axis Horizontal Reflection Reflect in y-axis Vertical Dilation ) or compress ( ) vertically Horizontal Dilation Compress ( ) or stretch ( ) horizontally 2. Common DSE Exam Patterns Coordinate Changes: Questions often provide a point transformation of graph dse exercise
: Focus on Section B of Paper 1 and the late-question MCs in Paper 2 (typically Q35-Q40) where these concepts are frequently tested. Guided Tutorials DSE Transformations of Graphs Inside function: ( (x+2) ) → shift left by 2 units
Why? Because examiners rarely ask you to plot a basic ( y = x^2 ) graph. Instead, they present a complex variant: ( y = -2(x-3)^2 + 4 ). Without transformation skills, you will struggle. With them, you can analyze the vertex, axis of symmetry, and intercepts in seconds. ( g(x) = |(x+2-1)^2 - 4| - 3 = |(x+1)^2 - 4| - 3 )
💡 Tip: Always check the wording carefully. "Reflected across the x-axis" is a vertical change, while "reflected across the y-axis" is a horizontal change.
( g(x) = |(x+2-1)^2 - 4| - 3 = |(x+1)^2 - 4| - 3 ).
Let ( h(x) = (x+1)^2 - 4 ) → zero at ( x = 1, -3 ).
Domain of (\sqrt-x/3): (-x/3 \ge 0 \implies x \le 0)
Range: (\sqrt\dots \ge 0 \implies \sqrt\dots + 2 \ge 2)