Transformation Of Graph Dse Exercise Here

When ( y = f(2x) ), the domain is halved. When ( y = \sqrt-x ), domain becomes ( x \le 0 ). Always check domain in DSE long questions.

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

To solidify transformation skills, practice these past paper questions:

| Year | Paper | Question | Focus | |------|-------|----------|-------| | 2023 | 1 (Core) | Q.12 | Composite transformations (quadratic to cubic) | | 2022 | 2 (MCQ) | Q.28 | Horizontal vs vertical scaling in exponential graphs | | 2021 | M2 | Q.6b | Transformations and inflection points | | 2019 | 1 | Q.9 | Absolute value and translation | | 2018 | 2 | Q.33 | Sine graph: find amplitude, period, phase shift |

The figure shows ( y = f(x) ). Which of the following represents ( y = f(2x) + 1 )?

(A) Shift left 1, horizontal compression by 1/2
(B) Horizontal compression by 1/2, then shift up 1
(C) Shift right 1, horizontal stretch by 2
(D) Horizontal stretch by 2, shift down 1 transformation of graph dse exercise

When multiple transformations are applied, follow the order: Stretches → Reflections → Translations (SRT rule).

But easier: Work from inside to outside in function notation.

Example:
From (y = f(x)) to (y = -2f(3x + 6) + 4):

Order of operations:
Horizontal compression → Horizontal translation → Vertical stretch → Reflection → Vertical translation.

Starting from ( y = \sqrtx ):

Order matters – the stretch/reflection applies before the final vertical shift.

Let ( y = f(x) ) be the original function.

| Transformation | Equation | Effect | |---------------|----------|--------| | Horizontal shift (right (c)) | ( y = f(x - c) ) | Moves graph right by (c) units | | Horizontal shift (left (c)) | ( y = f(x + c) ) | Moves graph left by (c) units | | Vertical shift (up (c)) | ( y = f(x) + c ) | Moves graph up by (c) units | | Vertical shift (down (c)) | ( y = f(x) - c ) | Moves graph down by (c) units | | Reflection in x-axis | ( y = -f(x) ) | Flips vertically | | Reflection in y-axis | ( y = f(-x) ) | Flips horizontally | | Vertical stretch (factor (a>1)) | ( y = a f(x) ) | Stretches vertically | | Vertical compression ((0<a<1)) | ( y = a f(x) ) | Compresses vertically | | Horizontal stretch ((0<a<1)) | ( y = f(ax) ) | Stretches horizontally (careful) | | Horizontal compression ((a>1)) | ( y = f(ax) ) | Compresses horizontally |

Note for students: Horizontal transformations are "opposite" of intuition: ( f(x+2) ) shifts left, ( f(2x) ) compresses horizontally.

The transformation of graphs is not a topic to memorize—it is a skill to internalize through structured, repetitive exercise. DSE examiners frequently disguise transformations within function notation, composite functions, or trigonometric modeling. By mastering the exercise blueprint outlined above—starting with basic shifts, progressing to composites, and practicing reverse logic—you will turn graph transformations into a reliable scoring zone. When ( y = f(2x) ), the domain is halved

Final Exercise for You (Answer below):

The graph of ( y = 2^x ) is reflected in the line ( y = x ), then stretched vertically by factor 3, then translated 2 units down. Find the equation of the resulting curve.

Answer: Reflection in ( y=x ) gives inverse: ( y = \log_2 x ).
Then vertical stretch ×3: ( y = 3 \log_2 x ).
Then down 2: ( y = 3 \log_2 x - 2 ).

Now go forth and transform every graph the DSE throws at you!

Try these questions based on common HKDSE past paper patterns: Question 1: Multiple TransformationsGiven the function is changed to , describe the geometric transformation. Step 1: Rewrite in terms of The graph of ( y = \sqrtx )

Answer: A translation of 3 units to the right and 6 units upwards. Question 2: Coordinate ChangesA point lies on the curve . Find the new coordinates of under the transformation Horizontal change: means shift left by 3. New Vertical change: means reflect in x-axis (multiply y by -1). New Answer:

Question 3: Trigonometric GraphsIdentify the equation for a sine graph that has been shifted 2 units up and compressed horizontally by a factor of 2. Transformations of Graphs - GCSE Higher Maths