IB Maths AI HL Ahl 2 8 Hl Graph Transformations Questions

Practise recognising and applying ordered graph transformations, writing the transformed rule and verifying it with key points or defining features.

Exam points

Recognise translations, reflections and horizontal or vertical stretches from the placement of constants in f.
Apply composite graph transformations in the stated order and map key points or defining features.
Write the transformed function rule and verify it using intercepts, amplitude, asymptotes or another defining feature.

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Study AHL 2.8 (HL)—Graph transformations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 3]

The function f is defined by $f(x)=4 \ln (2 x-3)$ , where $x>\frac{3}{2}$ .
The graph of y=f(x) is obtained from the graph of $y=\ln x$ by a sequence of three transformations.

Describe fully these transformations, including the order in which they occur.

vertical stretch scale factor 4

Note: The vertical stretch can occur in any order.

EITHER
translation $\binom{3}{0}$ followed by horizontal stretch scale factor $\frac{1}{2}$

OR
horizontal stretch scale factor $\frac{1}{2}$ followed by translation $\binom{1.5}{0}$

Note: Award A1A0 in either approach, for correct transformations, but incorrect order.

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IB Maths AI HL Ahl 2 8 Hl Graph Transformations Questions question 1