Transformation Of Graph Dse Exercise May 2026

Transforming graphs is like giving a function a makeover. In the DSE (Hong Kong Diploma of Secondary Education) curriculum, these exercises test your ability to manipulate coordinates and understand how equations respond to "stretches," "reflections," and "shifts." 🚀 The Core Transformation Rules

: For quadratic transformations, converting the equation to vertex form makes identifying the translations much easier. 3. Recommended Practice Resources Past Papers transformation of graph dse exercise

• Equation: $y = f(-x)$
• Transformation: The graph is flipped horizontally.
• Mechanism: Every $x$-coordinate changes sign ($x \rightarrow -x$), while $y$-coordinates remain unchanged.

  Given ( f(x) = \sqrtx ) for ( x \ge 0 ). Sketch the graph of ( g(x) = -2\sqrt4-x ). Determine the domain of ( g(x) ). Transforming graphs is like giving a function a makeover

  • Apply multiple transforms in correct order.
  • Convert between stepwise transforms and single algebraic form.

  Translation (horizontal)

  | Transformation | Effect on Graph | Algebraic Change | |----------------|----------------|-------------------| | | Shift right by (a) units ((a>0)) | (y = f(x - a)) | | | Shift left by (a) units | (y = f(x + a)) | | Translation (vertical) | Shift up by (b) units ((b>0)) | (y = f(x) + b) | | | Shift down by (b) units | (y = f(x) - b) | | Reflection (x-axis) | Flip vertically | (y = -f(x)) | | Reflection (y-axis) | Flip horizontally | (y = f(-x)) | | Stretch (vertical) | Multiply y-values by (k) ((k>1) stretch, (0<k<1) compress) | (y = k f(x)) | | Stretch (horizontal) | Divide x-values by (k) (i.e., (y = f(x/k))) – careful: stretch factor (1/k) | (y = f\left(\fracxk\right)) or (y = f(k' x))? Let’s clarify: | | Horizontal stretch factor (a) (from y-axis) | Points: ((x,y) \to (ax, y)) | (y = f(x/a)) | | Horizontal compression factor (a) | Points: ((x,y) \to (x/a, y)) | (y = f(ax)) | Equation: $y = f(-x)$ Transformation: The graph is