The graph of \(y = \ln (x)\) is transformed into the graph of \(y = \ln \left( {2x + 1} \right)\) .

Describe two transformations that are required to do this.

Solve \(\ln \left( {2x + 1} \right) > 3\cos (x)\), \(x \in [0,10]\).

EITHER

translation of \( - \frac{1}{2}\) parallel to the \(x\)-axis

stretch of a scale factor of \(\frac{1}{2}\) parallel to the \(x\)-axis     A1A1

OR

stretch of a scale factor of \(\frac{1}{2}\) parallel to the \(x\)-axis

translation of \( - 1\) parallel to the \(x\)-axis     A1A1

Note: Accept clear alternative terminologies for either transformation.

[2 marks]

EITHER

\(1.16 < x < 5.71 \cup 6.75 < x \leqslant 10\)     A1A1A1A1

OR

]\(1.16\), \(5.71\)[  \(\cup\)  ]\(6.75\), \(10\)]     A1A1A1A1

Note: Award A1 for 1 intersection value, A1 for the other 2, A1A1 for the intervals.

[6 marks]

This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – Stretch and Translation - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note \(x = 10\) as an endpoint.

This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – Stretch and Translation - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note \(x = 10\) as an endpoint.