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

• Equation: $y = f(-x)$
• Transformation: The graph is flipped horizontally.
• Mechanism: Every $x$-coordinate changes sign ($x \rightarrow -x$), while $y$-coordinates remain unchanged.

  Solution

  (a) ( y = f(x) + 3 )
  (b) ( y = f(x - 2) )
  (c) ( y = f(x + 1) - 4 )

  3. Worked Examples (DSE Style)

  Example 1: Combined Transformation

  Given ( f(x) = x^2 ), sketch ( g(x) = -2f(x+1) + 3 ).