Transformation Of Graph Dse Exercise
Instead of tracking the entire curve visually, track specific "anchor points" such as vertices, -intercepts, or -intercepts. If a point , it becomes , it becomes , it becomes Step 3: Handle the "Inside" Operations Carefully When converting , always factor out the coefficient of first to clearly see the true horizontal shift. Example: Transform Rewrite it as
is compressed horizontally to half its original width and then shifted upwards by 2 units to form . Find the new equation of in the form 4. Solutions and Explanations Answer 1: A Translate 3 units left →f(x+3)right arrow f of open paren x plus 3 close paren Step 2: Reflect in the -axis (multiply the whole function by -1negative 1
| Transformation | New Equation | Effect on Graph | | :--- | :--- | :--- | | | $y = f(x) + k$ | Shift up by $k$ units (if $k > 0$). | | | $y = f(x) - k$ | Shift down by $k$ units. | | Horizontal Translation | $y = f(x - k)$ | Shift right by $k$ units. | | | $y = f(x + k)$ | Shift left by $k$ units. | | Reflection | $y = -f(x)$ | Reflect about the x-axis . | | | $y = f(-x)$ | Reflect about the y-axis . | | Scaling (Stretch/Compress) | $y = k \cdot f(x)$ | Vertical stretch by factor $k$ (if $k > 1$). | | | $y = f(kx)$ | Horizontal compression by factor $\frac1k$. | transformation of graph dse exercise
. Apply the changes to that one point to see where the new graph should be.
Apply both shifts to the original point . . ✅ Final Answer The coordinates of the new minimum point are . Instead of tracking the entire curve visually, track
:
I can walk you through a specific example if you provide the coordinates! Find the new equation of in the form 4
Understanding Graph Transformations: A Complete DSE Guide Graph transformation is a core topic in the HKDSE Mathematics (Compulsory Part) syllabus. It tests your ability to manipulate functions visually and algebraically. Mastering this topic requires a clear understanding of four primary operations: translation, reflection, stretching, and compressing.
DSE Mathematics Core (Compulsory Part) Learning Objective: To understand and apply transformations (translation, reflection, scaling) to function graphs.
—visually shift, stretch, or reflect its graph on the Cartesian plane. The Four Pillars of Transformation
Below are exercises modeled on actual DSE questions. Try each before revealing the solution.