# Exam-Style Question on Transformation of Graphs

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 358. This question is similar to one that appeared on an IB Standard paper in 2011. The use of a calculator is not allowed.

Two functions are defined as follows: $$f(x) = 2\ln x$$ and $$g(x) = \ln \frac{x^2}{3}$$.

(a) Express $$g(x)$$ in the form $$f(x) - \ln a$$ , where $$a \in {{\mathbb{Z}}^ + }$$ .

(b) The graph of $$g(x)$$ is a transformation of the graph of $$f(x)$$ . Give a full geometric description of this transformation.

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