Transformation Of Graph Dse Exercise Info

Given ( y = f(x) ), and ( a > 0 ):

These move the graph without changing its shape or orientation. , the graph moves , it moves . This affects the -coordinates directly. Horizontal: . This is often counter-intuitive: moves the graph 2. Reflections (Flipping) Across the x-axis: -value is negated, "flipping" the graph upside down. Across the y-axis: -value is negated, "flipping" the graph sideways. 3. Scaling (Stretching/Compressing) , the graph stretches vertically. If , it compresses. Horizontal: transformation of graph dse exercise

. Find the new coordinates of this point after the transformation . The term Given ( y = f(x) ), and (

Changes made inside the function's argument counter-intuitively affect the -coordinates. The graph moves opposite to the sign. shifts the graph to the left by Horizontal Translation Rightward: shifts the graph to the right by Horizontal Stretching/Compressing: compresses the graph horizontally by a factor of 1k1 over k end-fraction , and stretches it if Reflections Reflections flip the graph across the coordinate axes. Reflection across the x-axis: negates all -values, flipping the graph vertically. Reflection across the y-axis: negates all -values, flipping the graph horizontally. 2. Systematic Workflow for Successive Transformations Horizontal:

Graph: The parabola opens upward with a vertex at (0, 3).

To solve DSE Paper 1 (Conventional) and Paper 2 (MC) questions quickly, categorize every transformation into one of two groups Outside the bracket ( transformations. They affect the -coordinates and are (they do exactly what you expect) shifts the graph by 3 units Inside the bracket ( Horizontal transformations. They affect the -coordinates and are Counter-Intuitive (they do the opposite of what you expect) shifts the graph by 2 units Common DSE Transformation Patterns

, the graph (becomes flatter) by a factor of Horizontal Scaling: