Transformation Of Graph Dse Exercise May 2026

DSE often asks: Given the image graph, find the pre-image function.

Question 3:
The graph of ( y = f(x) ) is translated 3 units right and then reflected in the y-axis to become ( y = \sqrt4 - x^2 ). Find ( f(x) ).

Step-by-step reasoning:
Let transformations be applied to ( f(x) ): transformation of graph dse exercise

Thus ( f(x) = \sqrt4 - (x+3)^2 ).

Q: 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. DSE often asks: Given the image graph, find

✅ Answer: A (f(2x) → compress horizontally by 1/2; +3 → shift up).

The figure shows ( y = f(x) ). Which of the following represents ( y = f(2x) + 1 )? Thus ( f(x) = \sqrt4 - (x+3)^2 )

(A) Shift left 1, horizontal compression by 1/2
(B) Horizontal compression by 1/2, then shift up 1
(C) Shift right 1, horizontal stretch by 2
(D) Horizontal stretch by 2, shift down 1

Answers: