On the same diagram sketch the graph of \(y = - f(x)\) .

Let \(g(x) = f(x + 3)\) .

(i)     Find \(g( - 3)\) .

(ii)    Describe fully the transformation that maps the graph of f to the graph of g.

     M1A1     N2

Note: Award M1 for evidence of reflection in x-axis, A1 for correct vertex and all intercepts approximately correct.

(i) \(g( - 3) = f(0)\)     (A1)

\(f(0) = - 1.5\)     A1     N2

(ii) translation (accept shift, slide, etc.) of \(\left( {\begin{array}{*{20}{c}}
{ - 3}\\
0
\end{array}} \right)\)     A1A1     N2

[4 marks]

This question was reasonably well done. Many recognized the graph of \( - f(x)\) as a reflection in a horizontal line, but fewer recognized the x-axis as the mirror line.

A fair number gave \(g( - 3) = f(0)\) , but did not carry through to \(f(0) = - 1.5\) . The majority of candidates recognized that moving the graph of \(f(x)\) by 3 units to the left results in the graph of \(g(x)\) , but the language used to describe the transformation was often far from precise mathematically.