Transformation Of Graph Dse Exercise

The transformation of graphs is a fundamental topic in the DSE (Diploma of Secondary Education) Mathematics curriculum. Mastering this area is not just about memorizing formulas; it is about developing a visual intuition for how functions behave under various algebraic "stresses." Core Concepts of Graph Transformation

  • Example: If $y = x^2$ becomes $y = x^2 + 2$, every point on the parabola moves up 2 units.
  1. Node Renaming: Renamed node C to F.
  2. Edge Addition: Added a new edge between nodes B and D.
  3. Edge Deletion: Deleted edge EA.
  4. Node Merging: Merged nodes A and E into a single node, AE.
  5. Node Splitting: Split node AE into two separate nodes, A and E.
  • Key transformation rules.
  • Step-by-step exercises.
  • Graphical interpretation practice.
  • Mixed exercise set (DSE style).

Example 1: Combined Transformation

  1. ( y = -|x - 4| )
  2. ( y = \frac12|x + 3| )
  3. ( y = |-x| + 1 ) (same as ( y = |x| + 1 ) due to symmetry)

Try these questions to simulate the DSE environment. Solutions follow below. Question 1 (Multiple Choice Style) The graph of is translated 3 units to the left and then reflected in the -axis. Let transformation of graph dse exercise

Question:

The graph of ( y = f(x) ) passes through (2, 3). It is transformed as follows: Step 1: Reflect in y-axis. Step 2: Stretch vertically by factor 3. Step 3: Shift left 1 unit and up 2 units. The transformation of graphs is a fundamental topic