Transformation Of Graph Dse Exercise May 2026

Sketch ( y = |x^2 - 4| - 1 ). How many x-intercepts?

A and D are equivalent and correct. Reflection first: ( y = -\sin x ), then +2. Exercise Set 2: Finding the Original Graph (Reverse Transformation) DSE often asks: Given the image graph, find the pre-image function. transformation of graph dse exercise

Stationary points occur when ( g'(x)=0 ). ( g(x) = 2f(1-x) + 1 ) ( g'(x) = 2 \cdot f'(1-x) \cdot (-1) = -2 f'(1-x) ) Set ( g'(x)=0 \implies f'(1-x)=0 ). Sketch ( y = |x^2 - 4| - 1 )

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. Part 1: The Four Pillars of Graph Transformation (DSE Core) Before tackling complex exercises, let’s establish the foundational rules. Assume the original graph is ( y = f(x) ). Reflection first: ( y = -\sin x ), then +2

Introduction: Why Graph Transformations Matter in DSE In the Hong Kong DSE Mathematics examination, the ability to manipulate and interpret graphs is not merely a mechanistic skill—it is a visual language. Questions involving transformation of graphs appear consistently across Papers 1 (Conventional) and 2 (MCQ), as well as in the M2 Calculus paper.

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 ).