IB Maths AI HL 2.8 Graph transformations Question Bank

Practise IB Mathematics HL 2.8 by applying graph transformations methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[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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AHL 2.8 (HL)—Graph transformations question 1