DSE questions rarely ask for a single transformation. They usually involve a sequence of movements. The order in which you apply these transformations matters immensely, especially when combining horizontal shifts and horizontal scaling.
Example: From (y = f(x)) to (y = -2f(3x + 6) + 4):
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Graph transformation exercises in DSE test conceptual clarity, not just plotting. Mastery requires:
| New equation | Meaning | |--------------|---------| | (y = f(x-a) + b) | Right a, up b | | (y = -f(x)) | Reflect in x-axis | | (y = f(-x)) | Reflect in y-axis | | (y = k f(x)) | Vertical stretch (k>1) / compress (0<k<1) | | (y = f(ax)) | Horizontal compress (a>1) / stretch (0<a<1) | | (y = f(ax + b)) | First factor: (a(x + b/a)) → compress by (1/a), then shift left (b/a) | DSE questions rarely ask for a single transformation
Sketch (y = 2\sin(3x - \pi) + 1) and (y = -\ln(2x) + 3).
When tackling a graph transformation exercise in a DSE environment (such as IBM Cloud Pak for Data, Apache Spark GraphX, or Neo4j Graph Data Science), follow this structured workflow: Step 1: Analyze the Source Graph Profile Example: From (y = f(x)) to (y =
In the HKDSE exam, you will rarely face a single, isolated transformation. The real challenge lies in correctly sequencing multiple transformations. .
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Here are the solutions to the exercises, along with step-by-step explanations to help you understand the how and the why .