Transformation Of Graph Dse Exercise -

The graph of ( y = \sqrtx ) is transformed into ( y = -2\sqrtx - 3 + 1 ).
Describe the transformations in correct order.

Question: The graph of $y = f(x)$ undergoes the following transformations in order:

Write down the final equation.

👀 Think about it first!

. . .

Solution: We apply the transformations step-by-step. Let the original equation be $y = f(x)$.

In the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics curriculum, the transformation of graphs is a foundational topic that bridges algebra and geometry. Mastery of this exercise requires more than memorizing formulas; it demands an understanding of how "inside" and "outside" operations on a function manipulate points in a coordinate plane. 1. The Core DSE Transformation Types

DSE exercises typically categorize transformations into four primary movements: Graph Transformations | Graphs | Maths | FuseSchool

Mastering the Transformation of Graphs: A Comprehensive Guide for DSE Students

In the Hong Kong Diploma of Secondary Education (DSE) Mathematics curriculum, the Transformation of Graphs is a cornerstone topic. It bridges the gap between basic algebra and visual calculus. Whether you are tackling Paper 1 (Long Questions) or Paper 2 (Multiple Choice), mastering how a function morphs into is essential for securing a 5** rating.

This article breaks down the core concepts and provides a structured "DSE-style" exercise to test your skills. 1. The Four Pillars of Transformation transformation of graph dse exercise

Every transformation can be categorized into one of four movements. To succeed, you must distinguish between Vertical changes (affecting the output ) and Horizontal changes (affecting the input A. Translation (Shifting) Vertical Shift: +kpositive k moves the graph up; −knegative k moves it down. Horizontal Shift: Counter-intuitive rule: moves the graph right, while moves it left. B. Reflection (Flipping) Reflection in x-axis: The graph flips upside down (all -coordinates change sign). Reflection in y-axis: The graph flips horizontally (left becomes right). C. Scaling (Enlarging/Compressing) Vertical Stretch/Compression: , the graph stretches vertically. If , it compresses. Horizontal Stretch/Compression: Counter-intuitive rule: If , the graph compresses horizontally by a factor of , it stretches. 2. Common DSE Pitfalls to Avoid The "Opposite" Rule for : Students often forget that operations inside the bracket

act in the opposite direction of the sign. Always remember: "Inside the bracket, do the opposite."

Order of Transformations: If a graph undergoes multiple transformations, the order matters. Generally, follow the order of operations: deal with horizontal changes inside the bracket first, then vertical changes outside.

Vertex Changes: For quadratic graphs, always track what happens to the vertex

. It is often the easiest way to identify the correct transformation in MC questions. 3. Transformation of Graph: DSE Practice Exercise

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

be the equation of the resulting graph. Which of the following is Question 2 (Short Question Style) .(a) Find the coordinates of the vertex of .(b) The graph of

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 Step 1: 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

→−f(x+3)right arrow negative f of open paren x plus 3 close paren (a) By completing the square: . The vertex is .(b) Step 1: Horizontal compression by factor 2 means we replace Step 2: Shift up by 2 units (add 2 to the result). Final Answer: Conclusion

The transformation of graphs is a logical puzzle. By identifying whether a change is "inside the bracket" or "outside the bracket," you can predict the movement of any function. For your DSE revision, focus on practicing trigonometric transformations (sine and cosine waves), as these frequently appear in the harder sections of Paper 2. The graph of ( y = \sqrtx )

Are you struggling with a specific type of transformation or a tricky past paper question?

In the HKDSE Mathematics curriculum, Transformation of Graphs is a critical topic frequently appearing in Paper 1 (Section A and B) and Paper 2 (Multiple Choice). It involves changing a parent function

through translation, reflection, and dilation (enlargement/contraction). 1. Summary of Transformation Rules

The key to mastering this topic is distinguishing between "Inside" (horizontal) and "Outside" (vertical) changes. Transformation Type Effect on Graph Effect on Coordinates Vertical Translation Move up by Move down by Horizontal Translation Move left by Move right by Vertical Reflection Reflect in x-axis Horizontal Reflection Reflect in y-axis Vertical Dilation ) or compress ( ) vertically Horizontal Dilation Compress ( ) or stretch ( ) horizontally 2. Common DSE Exam Patterns Coordinate Changes: Questions often provide a point

and ask for the new coordinates after a series of transformations.

Multiple-Choice Identification: You may be given a graph and asked to identify which function ( ) represents it. A common trick is checking the -intercept ( ) or specific vertices.

Order of Operations: If multiple transformations are applied to

, follow the order of arithmetic (multiplication/reflection before addition/subtraction). For , the order is often counter-intuitive (e.g., involves a shift then a stretch). 3. Sample DSE-Style Exercise Problem:The figure shows the graph of . The curve has a maximum point at and crosses the x-axis at Sketch the graph of . State the new coordinates of , state the new coordinates of Solution:

In the HKDSE Mathematics (Compulsory Part) syllabus, the Transformation of Graphs

typically involves four main types of operations: translation, reflection, and enlargement/reduction (stretching/compressing). Summary of Graph Transformations Transformation Type Algebraic Change Visual Effect Vertical Translation Horizontal Translation Reflection (x-axis) Flips upside down Reflection (y-axis) Flips left-to-right Vertical Stretch/Scale Enlarges ( ) or contracts ( ) along y-axis Horizontal Stretch/Scale Enlarges ( ) or contracts ( ) along x-axis DSE Style Exercise: Multiple Choice The graph of has a vertex at Write down the final equation

, what are the coordinates of the new vertex on the graph of Step 1: Identify Horizontal Change Inside the brackets, we see . In DSE math, changes inside the bracket affecting

are "opposite" to their sign. A minus sign indicates a movement to the Add 3 to the original x-coordinate. Calculation: Step 2: Identify Vertical Change Outside the brackets, we see positive 1 . Changes outside the function affecting follow the sign directly. A plus sign indicates a movement Add 1 to the original y-coordinate. Calculation: Step 3: State New Coordinates Combining the new values, the vertex moves from Correct Answer: Order of Operations Caution When multiple transformations occur, the order matters . For example,

(reflect then shift up) results in a different graph than reflecting after shifting. In DSE Paper 2 (MC), always carefully track each step sequentially. Save My Exams Answer Restatement: The new vertex for starting from

. This is achieved by shifting the original point 3 units to the right and 1 unit up. trigonometric graphs

| Error | Correction | |-------|-------------| | ( f(x+2) ) shifts right | Shifts left | | ( f(2x) ) stretches horizontally | Compresses horizontally | | Order of transformations: shift then reflect | Do reflections/stretches before shifts when inside f | | Forgetting domain changes after horizontal shifts/reflections | Always check domain for root/log functions |

Start from ( f(x) = \sqrtx ).

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Given ( f(x) = |x| ), write the equation for:

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