Transformation Of Graph Dse Exercise [exclusive] Jun 2026

The figure shows ( y = f(x) ). Which of the following represents ( y = f(2x) + 1 )?

Below is a comprehensive breakdown of each transformation, how it affects the graph, and the corresponding changes to the equation y = f(x) . transformation of graph dse exercise

Remember: ( y = A \sin(Bx + C) + D )

Reflection involves flipping the graph across a specific axis. The figure shows ( y = f(x) )

Download our complete 50-question transformation worksheet with step-by-step video solutions. (Link to your resource) Remember: ( y = A \sin(Bx + C)

Look at the structure. If we take the original equation and factor 3 from the right-hand side: [ y = 3(x^2 - 3x + 5) ] This is exactly the same as the second graph. Therefore, the transformation is simply a vertical stretch by a factor of 3 . This question type requires you to look beyond the surface and recognize the underlying pattern.

| Transformation | Effect on graph | Mapping of point ((x, y)) | |----------------|----------------|-----------------------------| | ( y = f(x) + a ) | Shift by (a) | ((x, y) \to (x, y+a)) | | ( y = f(x) - a ) | Shift down by (a) | ((x, y) \to (x, y-a)) | | ( y = f(x+a) ) | Shift left by (a) | ((x, y) \to (x-a, y)) | | ( y = f(x-a) ) | Shift right by (a) | ((x, y) \to (x+a, y)) | | ( y = a f(x) ) | Vertical stretch (if (a>1)) or compression ((0<a<1)) | ((x, y) \to (x, a y)) | | ( y = f(ax) ) | Horizontal compression (if (a>1)) or stretch ((0<a<1)) | ((x, y) \to (\fracxa, y)) | | ( y = -f(x) ) | Reflection in x‑axis | ((x, y) \to (x, -y)) | | ( y = f(-x) ) | Reflection in y‑axis | ((x, y) \to (-x, y)) |