Reflection involves flipping the graph across a specific axis.
A. Reflection about the x-axis
B. Reflection about the y-axis
The transformation of graphs is not a topic to memorize—it is a skill to internalize through structured, repetitive exercise. DSE examiners frequently disguise transformations within function notation, composite functions, or trigonometric modeling. By mastering the exercise blueprint outlined above—starting with basic shifts, progressing to composites, and practicing reverse logic—you will turn graph transformations into a reliable scoring zone.
Final Exercise for You (Answer below):
The graph of ( y = 2^x ) is reflected in the line ( y = x ), then stretched vertically by factor 3, then translated 2 units down. Find the equation of the resulting curve.
Answer: Reflection in ( y=x ) gives inverse: ( y = \log_2 x ).
Then vertical stretch ×3: ( y = 3 \log_2 x ).
Then down 2: ( y = 3 \log_2 x - 2 ).
Now go forth and transform every graph the DSE throws at you!
Try these questions based on common HKDSE past paper patterns: Question 1: Multiple TransformationsGiven the function is changed to , describe the geometric transformation. Step 1: Rewrite in terms of transformation of graph dse exercise
Answer: A translation of 3 units to the right and 6 units upwards. Question 2: Coordinate ChangesA point lies on the curve . Find the new coordinates of under the transformation Horizontal change: means shift left by 3. New Vertical change: means reflect in x-axis (multiply y by -1). New Answer:
Question 3: Trigonometric GraphsIdentify the equation for a sine graph that has been shifted 2 units up and compressed horizontally by a factor of 2. Transformations of Graphs - GCSE Higher Maths
A progressive set of exercises (4 weeks) for secondary students preparing for Hong Kong DSE (or equivalent) on graph transformations: translations, reflections, stretches/compressions, and combinations. Each week has objectives, worked examples, practice questions, and answers.
The graph of ( y = \sqrtx ) is transformed into ( y = -2\sqrtx - 3 + 1 ).
Describe the transformations in correct order. Reflection involves flipping the graph across a specific
Question 4 (Paper 1, 6 marks):
The graph of ( y = \sqrtx ) is stretched vertically by factor 2, then reflected in the x-axis, then translated 1 unit left. Write the final equation.
Solution:
Start: ( y = \sqrtx )
Final answer: ( y = -2\sqrtx+1 )
❗Note: If translation occurred before reflection, the result differs. Order strictly follows sequence described. The transformation of graphs is not a topic