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
) usually behave the opposite of what you might expect. For example, adding to moves the graph left, and multiplying transformation of graph dse exercise
Translation involves moving the entire graph without changing its shape or orientation. , the graph moves up , the graph moves down Horizontal Shift: , the graph moves right units (e.g., moves 3 units right). , the graph moves left units (e.g., moves 3 units left). 2. Reflection: Flipping the Graph Reflection creates a mirror image of the original function. Reflection across the x-axis: All y-values change signs. The top becomes the bottom. Reflection across the y-axis: The transformation of graphs is a fundamental topic
, it is a horizontal compression (the graph squishes toward the y-axis). , the graph moves up , the graph
Draw the new graph and check if the changes match the algebraic operations (e.g., did a actually flip it upside down?). Sample DSE Exercise Problem: Let be a function. If the graph of
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