CAIE P1 2021 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicFunction Transformations
TypeExpress function using transformations

6 Functions f and g are both defined for \(x \in \mathbb { R }\) and are given by $$\begin{aligned} & \mathrm { f } ( x ) = x ^ { 2 } - 2 x + 5
& \mathrm {~g} ( x ) = x ^ { 2 } + 4 x + 13 \end{aligned}$$
  1. By first expressing each of \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\) in completed square form, express \(\mathrm { g } ( x )\) in the form \(\mathrm { f } ( x + p ) + q\), where \(p\) and \(q\) are constants.
  2. Describe fully the transformation which transforms the graph of \(y = \mathrm { f } ( x )\) to the graph of \(y = \mathrm { g } ( x )\).