For the graph of f:

(i)     write down the \(y\)-intercept;

(ii)     find the \(x\)-intercept;

(iii)     write down the equation of the horizontal asymptote.

On the following grid, sketch the graph of \(f\), for \( - 4 \leqslant x \leqslant 4\).

(i)     \(y =  - 1\)     A1     N1

(ii)     valid attempt to find \(x\)-intercept     (M1)

eg\(\,\,\,\,\,\)\(f(x) = 0\)

1.38629     A1     N2

\(x = 2\ln 2{\text{ (exact), }}1.39\)

(iii)     \(y =  - 2\) (must be equation)     A1     N1

     A1A1A1     N3

[3 marks]

In part a), most candidates were successful at finding the intercepts with the x and y axis, though many failed to write the horizontal asymptote as an equation. Some candidates gave the answer for the horizontal asymptote as \(y \ne  - 2\).

For part b), a considerable number of candidates could sketch the exponential function providing an approximately correct shape, although many of them did not use the correct domain, making it go beyond \(x = 4\). Others plotted an incorrect value of \(y\) at \(x = 4\), resulting in the loss of a mark.

Considering that all the question requires from students is to copy the graph off the GDC, it is important to stress which are the features that cannot be missed.