Transformation Of Graph Dse Exercise __full__

For your HKDSE mathematics revision, a particularly "useful feature" for mastering Graph Transformations "Inside vs. Outside" rule

Typical DSE approach:

(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 transformation of graph dse exercise

4. Combined Transformations (Order Matters!)

For ( y = a f(b(x - h)) + k ), the correct DSE order is: For your HKDSE mathematics revision, a particularly "useful

Pitfall 3: Forgetting Domain Changes

When ( y = f(2x) ), the domain is halved. When ( y = \sqrt-x ), domain becomes ( x \le 0 ). Always check domain in DSE long questions. "Left by 3 units": Replace $x$ with $(x + 3)$

Exercise Set 4: Transforming Derivatives

Question 5 (M2 Type):
Given ( f(x) = x^3 - 3x ). Let ( g(x) = 2f(1-x) + 1 ). Find the x-coordinates of stationary points of ( g ).

A. $y = 2f(2x)$ B. $y = \frac12f(2x)$ C. $y = 2f(\frac12x)$ D. $y = \frac12f(\frac12x)$