Transformation Of Graph Dse Exercise ❲8K 2026❳

f(x) = -((x - 2)^2 + 3) → f(x) = -2((x - 2)^2 + 3)

Then: ( y = -f(x+1) ) → Step 1: ( f(x+1) ) shifts left by 1. Step 2: Negative sign reflects in x‑axis. 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 ). f(x) = -((x - 2)^2 + 3) →

: Reverse steps backward. Let (g(x) = 2x^2 - 4x + 5). Reverse vertical stretch (divide by 2): (h(x) = x^2 - 2x + 2.5) Reverse shift right 3 (shift left 3): (f(x) = h(x+3) = (x+3)^2 - 2(x+3) + 2.5) Simplify: (x^2 + 6x + 9 - 2x - 6 + 2.5 = x^2 + 4x + 5.5) Thus (f(x) = x^2 + 4x + 5.5). Then vertical stretch ×3: ( y = 3 \log_2 x )