This study notes covers Worked Examples within Graph Transformations for GCSE Mathematics. Revise Graph Transformations in Graphs for GCSE Mathematics with 14 exam-style questions and 1 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 4 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 3 of 4
Practice
14 questions
Recall
1 flashcards
Worked Examples
Example 1
The graph of y = x² is translated 3 units to the right. Write the equation of the transformed graph.
Solution
Translate right 3 means use (x − 3)
New equation: y = (x − 3)²
Example 2
A graph has equation y = f(x). The point (2, 5) lies on this graph. After the transformation y = 2f(x), what are the new coordinates of this point?
Step 1: Understand the transformation
y = 2f(x) means multiply all y-values by 2
This is a vertical stretch by factor 2
Step 2: Apply to the x-coordinate
Vertical stretch doesn't affect x-coordinates
x stays as 2
Step 3: Apply to the y-coordinate
Original y-value: 5
New y-value: 5 × 2 = 10
Step 4: State the new coordinates
The transformed point is (2, 10)
Example 3
The graph y = f(x) passes through the point (4, -3). Find the coordinates of this point after the combined transformations: first a reflection in the x-axis, then a translation 5 units left.
Step 1: Apply the first transformation (reflection in x-axis)
Reflection in x-axis: y = -f(x)
This changes the sign of y-coordinates
After reflection: (4, -3) becomes (4, 3)
Step 2: Apply the second transformation (translation left 5)
Translation left 5: y = f(x + 5)
This subtracts 5 from x-coordinates
x-coordinate: 4 - 5 = -1
y-coordinate stays: 3
Step 3: Write the equation of the final graph
Starting with y = f(x)
After reflection: y = -f(x)
After translation: y = -f(x + 5)
Step 4: State the final answer
The point (4, -3) transforms to (-1, 3)
The equation becomes y = -f(x + 5)
Keep building this topic
Read this section alongside the surrounding pages in Graph Transformations. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Graph Transformations
The graph of y = f(x) is transformed to y = f(x) + 3. Which of the following describes this transformation?
Describe fully each of the following transformations of y = f(x): (a) y = 3f(x) (b) y = f(2x) (c) y = f(x) - 5
Quick Recall Flashcards
14 questions on Graph Transformations — practise free
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