When multiple transformations are applied, always perform stretches and reflections before translations, unless parentheses dictate otherwise.
M(1,8)→(1,8−3)=(1,5)cap M open paren 1 comma 8 close paren right arrow open paren 1 comma 8 minus 3 close paren equals open paren 1 comma 5 close paren transformation of graph dse exercise
Half period → horizontal stretch? No: half period means frequency doubled → ( y = \sin(2x) ). Then point (0,0) maps to (0,-1) → vertical shift down 1. But check: ( y = \sin(2x) - 1 ) at x=0 gives -1. Yes. No reflection. Final: Horizontal compression by factor 1/2, then shift down 1. Then point (0,0) maps to (0,-1) → vertical shift down 1
is inside the bracket. This represents a . Since it is +2positive 2 , we move the graph left by 2 units . Math: Subtract -coordinates. No reflection
For more structured practice, you can download specialized worksheets from sites like MathsPercyYeung Physics & Maths Tutor based on these DSE patterns? HKDSE Graph Transformations Guide | PDF - Scribd