OCR C3 2009 January — Question 7

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2009
SessionJanuary
TopicFunction Transformations
TypeMultiple transformations in sequence

7
\includegraphics[max width=\textwidth, alt={}, center]{c940af95-e291-402a-856c-9090d13163d5-3_419_700_1809_721} The diagram shows the curve \(y = \mathrm { e } ^ { k x } - a\), where \(k\) and \(a\) are constants.
  1. Give details of the pair of transformations which transforms the curve \(y = \mathrm { e } ^ { x }\) to the curve \(y = \mathrm { e } ^ { k x } - a\).
  2. Sketch the curve \(y = \left| \mathrm { e } ^ { k x } - a \right|\).
  3. Given that the curve \(y = \left| \mathrm { e } ^ { k x } - a \right|\) passes through the points \(( 0,13 )\) and \(( \ln 3,13 )\), find the values of \(k\) and \(a\).