.This means the horizontal shift is actually , not 4.
Answers:
Before tackling complex exercises, let’s establish the foundational rules. Assume the original graph is ( y = f(x) ). transformation of graph dse exercise
: The graph of (y = f(x)) is transformed to (y = f(2x) + 3). Which of the following is correct? A. Horizontal compression by factor 1/2, vertical shift up 3. B. Horizontal stretch by factor 2, vertical shift up 3. C. Horizontal compression by factor 2, vertical shift up 3. D. Horizontal stretch by factor 1/2, vertical shift up 3. : The graph of (y = f(x)) is transformed to (y = f(2x) + 3)
✅ Answer: A (f(2x) → compress horizontally by 1/2; +3 → shift up). Horizontal compression by factor 1/2, vertical shift up 3
The graph of ( y = f(x) ) is shifted left by 2, then reflected in the y‑axis, resulting in ( y = x^2 + 1 ). Find ( f(x) ).