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.