Transformation Of Graph Dse Exercise _hot_ -

or an intercept) and apply the transformations to that point to see where it lands. practice problem

A progressive set of exercises (4 weeks) for secondary students preparing for Hong Kong DSE (or equivalent) on graph transformations: translations, reflections, stretches/compressions, and combinations. Each week has objectives, worked examples, practice questions, and answers.

This exercise is typical of multiple-choice questions (Paper 1). You are given the graph of ( y = f(x) ) (in blue) and the graph of ( y = g(x) ) (in red). Determine the relationship between them.

[Base Function: f(x)] │ ▼ 1. Horizontal Shifting ───► f(x ± c) │ ▼ 2. Horizontal Stretching/Reflecting ───► f(a·x ± c) │ ▼ 3. Vertical Stretching/Reflecting ───► b · f(a·x ± c) │ ▼ 4. Vertical Shifting ───► b · f(a·x ± c) ± d Step-by-Step Order Workflow Shift left or right first. transformation of graph dse exercise

Multiplying by a coefficient changes the steepness or width of the curve. . Stretches vertically if ; compresses if . Coordinates become Horizontal Scale: . Compresses horizontally if ; stretches if . Coordinates become Step-by-Step DSE Exercise Walkthrough

Horizontal transformations are counter-intuitive . ( y = f(x - 2) ) moves the graph right , not left. ( y = f(2x) ) compresses horizontally (period halves), not expands.

Mixing vertical shifts with vertical stretches alters the final position. Always perform multiplications before additions. Incorrectly Handling : When given an expression like , you must factor out the 2 first: or an intercept) and apply the transformations to

So x‑intercepts: ( -1 - \sqrt7,; -2,; 0,; -1 + \sqrt7 ).

So the new graph will pass through ( (-1, 0) ) and be inverted vertically.

, you must perform the horizontal stretch/compression before the horizontal shift. Consistency in your chosen framework prevents errors. Step-by-Step DSE Exercise Walkthrough This exercise is typical of multiple-choice questions (Paper

The you are required to use (Adjacency Matrix, Adjacency List, or Edge List). The programming language you prefer for code examples. Share public link

, the parabola opens downward, and it is narrower than the original parent function. Common Pitfalls in DSE Graphing Exercises

// Moving a purchase record from a flat node structure to a direct relationship MATCH (u:User)-[:MADE_TRANSACTION]->(t:Transaction)-[:FOR_PRODUCT]->(p:Product) CREATE (u)-[r:BOUGHT date: t.date, amount: t.amount]->(p) DETACH DELETE t; Use code with caution. Step 4: Validate Graph Integrity

Example 2: Graphical Matching (Paper 2 Multiple Choice Style) The figure shows the graph of . If the graph is transformed into , how does the new graph look compared to the old one? Solution: