Transformation Of Graph Dse Exercise |verified| 【Must Read】

In DSE exams, questions often combine multiple transformations. For example: $$y = a \cdot f(bx + c) + d$$

Let ( g(x) = |f(x+2)| - 3 ). If ( f(x) = (x-1)^2 - 4 ), (a) Find the x‑intercepts of ( g(x) ). (b) Sketch ( y = g(x) ). transformation of graph dse exercise

Transformations happening inside the function brackets (affecting (b) Sketch ( y = g(x) )

| 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)) | y) \to (x