Transformation Of Graph Dse Exercise Official

| Function | Effect of (y = f(x-a) + b) | Effect of (y = k f(x)) | |----------|-------------------------------|--------------------------| | Quadratic (x^2) | Vertex shifts to (a, b) | Stretch in y-direction | | Exponential (e^x) | Horizontal shift = growth starting point change | Changes growth rate | | Logarithmic (\ln x) | Vertical shift changes horizontal asymptote? No, log has vertical asymptote at x = a after shift | Vertical stretch changes steepness | | Sine ( \sin x) | Horizontal shift = phase shift | Vertical stretch = amplitude change |

Graph transformation is a fundamental topic in analytic geometry and function analysis. For DSE candidates, mastering graph shifts, reflections, stretches, and compressions is essential for solving complex function problems quickly without plotting every point. transformation of graph dse exercise

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 ). | Function | Effect of (y = f(x-a)