y=(−(x+2))2−3y equals open paren negative open paren x plus 2 close paren close paren squared minus 3
Which of the following represents the graph of ( y = -f(x+1) ) if ( y = f(x) ) is the graph below? (Here, imagine a decreasing exponential or a simple V‑shape; in DSE they give a sketch.)
These transformations focus on the data payloads carried by the vertices and edges rather than the shape of the network.
: Apply horizontal stretches/compressions first, followed by vertical ones. R - Reflection : Apply reflections across the axes. T - Translation : Apply horizontal and vertical shifts last. Tip for Horizontal Steps: If you have an expression like transformation of graph dse exercise
Then: ( y = -f(x+1) ) → Step 1: ( f(x+1) ) shifts left by 1. Step 2: Negative sign reflects in x‑axis.
To master graph transformations for the HKDSE (Mathematics Compulsory Part), you need to understand how algebraic changes to a function translate into physical movements on a coordinate plane. 1. Core Transformation Rules
Whether it’s a quadratic function, trigonometric curve, or an abstract ( y = f(x) ), examiners expect candidates to visualize how algebraic changes alter geometric shapes. This article provides a structured to mastering four core transformations: translation, reflection, scaling, and their composite applications. y=(−(x+2))2−3y equals open paren negative open paren x
: For this combined transformation, y = -f(2x+4) . First, factor the horizontal shift and stretch: y = -f(2(x+2)) .
: For Paper 2 multiple-choice questions, if you are unsure of the transformation, pick a clear point from the original graph (like the vertex or an intercept) and test which transformed equation satisfies the new coordinates. Completing the Square
DSE questions often combine multiple transformations into a single problem. The order of operations is critical to finding the correct answer. Sample Problem The graph of is compressed horizontally by a factor of , then shifted to the right by R - Reflection : Apply reflections across the axes
This comprehensive guide breaks down the core transformation rules, provides targeted DSE-style exercises, and outlines the exact step-by-step strategies you need to score full marks. 1. The Four Core Graph Transformations
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HKDSE questions rarely ask for just one transformation. They usually combine two or three shifts, reflections, or stretches.
The standard mathematical convention follows the order of operations, typically managed from the "inside out":
Treat the transformations step-by-step on the point The horizontal shift in moves the graph right by 3 units: The negative sign in reflects the graph across the -axis, changing the sign of the -coordinate: Question 4 Solution (a)