Transformation Of Graph Dse Exercise _hot_ May 2026

A transformation of a graph exercise in the DSE (Diploma of Secondary Education) typically focuses on how specific changes to an algebraic function—

10. Sample Exercise with Solution

Exercise:
The graph of (y = \sqrtx) is transformed by: transformation of graph dse exercise

• Example: $y = 2x^2$ is narrower than $y = x^2$.

• x-coordinates are halved: The graph is compressed horizontally.
  • ( x^2 - 4 = 1 \implies x^2 = 5 \implies x = \pm\sqrt5 )
  • ( x^2 - 4 = -1 \implies x^2 = 3 \implies x = \pm\sqrt3 )
    Total 4 x-intercepts.

  . . .

  1. Identify the base function – Is it ( x^2, \sqrtx, \sin x, e^x ), or an abstract ( f(x) )?
  2. Deconstruct the given equation – Write it in the form ( a f(b(x - h)) + k ).
  3. Apply transformations in correct order (HS, VS, HT, VT inside-to-outside: ( b(x-h) ) first, then ( a ), then ( k )).
  4. Check key points – Vertices, intercepts, asymptotes, period/amplitude for trig.
  5. Verify with a test point – Substitute ( x=0 ) or a known value from original graph.

  Answer: A and D are equivalent and correct. Reflection first: ( y = -\sin x ), then +2. A transformation of a graph exercise in the

  Solution: