Trig graphs test horizontal scaling (period change) and vertical scaling (amplitude) most intensely.
is a core topic in the HKDSE Mathematics (Compulsory Part) exam. Students must master how algebraic changes to a function's equation alter its visual graph. This comprehensive guide covers the essential transformation rules, breaks down complex multi-transformation problems, and provides practice exercises with step-by-step solutions to help you secure full marks. Core Principles of Graph Transformations
Now it's time to see if you've truly mastered the concepts. The best way to prepare for the HKDSE is to practice with authentic-style questions. Each exercise below is followed by a detailed, step-by-step solution to solidify your understanding.
Graph: The parabola opens upward with a vertex at (0, 3). transformation of graph dse exercise
Graph transformation refers to the process of changing the shape, position, or orientation of a graph. This can be achieved through various techniques, including translations, reflections, stretches, and compressions. These transformations can be applied to any type of graph, including linear, quadratic, polynomial, and trigonometric functions.
Start: ( y = \sqrtx )
Graph: The parabola opens downward with a vertex at (2, -6). Trig graphs test horizontal scaling (period change) and
Horizontally compressing to half its width means multiplying the inside variable by 2 (inverse behavior) Shifting upward by 1 unit adding 1 to the outside 4. Summary Cheat Sheet for DSE Revision Transformation Change in Equation Effect on Coordinates Shift Up Shift Down Shift Left Shift Right Reflect Over X-Axis Reflect Over Y-Axis Vertical Stretch ( ) Horizontal Compression ( )
—visually shift, stretch, or reflect its graph on the Cartesian plane. The Four Pillars of Transformation
-axis, which of the following is the equation of the resulting graph?A. Translate rightward by 2 units Reflect in the →right arrow multiply the outside by Correct Answer: C Question 4 Each exercise below is followed by a detailed,
Start: ( y = f(x) ) Reflect y-axis: ( y = f(-x) ) Vert stretch ×3: ( y = 3f(-x) ) Shift left 1: replace x with ( x+1 ) inside f: ( y = 3f(-(x+1)) = 3f(-x - 1) ) Shift up 2: ( y = 3f(-x - 1) + 2 )
A and D are equivalent and correct. Reflection first: ( y = -\sin x ), then +2.
These move the graph without changing its shape or orientation. , the graph moves , it moves . This affects the -coordinates directly. Horizontal: . This is often counter-intuitive: moves the graph 2. Reflections (Flipping) Across the x-axis: -value is negated, "flipping" the graph upside down. Across the y-axis: -value is negated, "flipping" the graph sideways. 3. Scaling (Stretching/Compressing) , the graph stretches vertically. If , it compresses. Horizontal: