Remember that actions inside the function function function argument (
y=(−(x+2))2−3y equals open paren negative open paren x plus 2 close paren close paren squared minus 3
Adding or subtracting a constant inside the function argument moves the graph horizontally. This movement is often counterintuitive. Rule: If ), the graph shifts to the right . If ), it shifts to the left . Coordinate Change: 3. Reflection (Flipping)
. Find the new coordinates of this point after the transformation . The term transformation of graph dse exercise
For ( y = a f(b(x - h)) + k ), the correct DSE order is:
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Are you trying to or sketch the new graph ? Remember that actions inside the function function function
If ( g(x) = -f(x) + 5 ), then the graph of ( f ) is: a) Reflected in x-axis and up 5 b) Reflected in y-axis and up 5 c) Reflected in x-axis and down 5 d) Reflected in y-axis and down 5
Try these questions based on common HKDSE past paper patterns : Given the function is changed to , describe the geometric transformation. Step 1: Rewrite in terms of
Use these to drill before exams.
Subtract 5 from the entire function:
The transformation of graphs is not just a DSE topic—it is a lens through which mathematicians view the world. Every parabola, sine wave, or exponential curve you encounter is a shifted, scaled, or reflected version of a parent function.
To find the vertex, rewrite the quadratic equation in vertex form by completing the square: y=x2−4x+1y equals x squared minus 4 x plus 1 If ), it shifts to the left
This comprehensive guide breaks down the rules of graph transformations, analyzes common DSE exam traps, and provides targeted exercise questions with detailed solutions to help you secure full marks. The Core Principles of Graph Transformations Every transformation affects either the input ( -values) or the output ( -values) of a function ( ) affect the graph vertically ( -direction) and follow common logic. Changes inside the function ( ) affect the graph horizontally ( -direction) and operate inversely to common intuition. Transformation Type Algebraic Notation Visual Effect on Graph Vertical Translation Shift up by Shift down by Horizontal Translation Shift left by Shift right by Reflection Reflect across the -axis (vertical flip) Reflect across the -axis (horizontal flip) Vertical Scaling Stretch vertically by factor Compress vertically by factor Horizontal Scaling Compress horizontally by factor 1k1 over k end-fraction Stretch horizontally by factor 1k1 over k end-fraction Common DSE Exam Traps to Avoid The Horizontal Shift Direction: Students frequently mistake