| Date | November 2014 | Marks available | 2 | Reference code | 14N.1.sl.TZ0.11 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Write down | Question number | 11 | Adapted from | N/A |
Question
Consider the functions \(f(x) = x + 1\) and \(g(x) = {3^x} - 2\).
Write down
(i) the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\);
(ii) the \(y\)-intercept of the graph of \(y = {\text{ }}g(x)\).
Solve \(f(x) = g(x)\).
Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).
Markscheme
(i) \(( - 1,{\text{ }}0)\) (A1)
Note: Accept \( - 1\).
(ii) \((0,{\text{ }} - 1)\) (A1) (C2)
Note: Accept \( - 1\).
\((x = ){\text{ }} - 2.96{\text{ }}( - 2.96135 \ldots )\) (A1)
\((x = ){\text{ }}1.34{\text{ }}(1.33508 \ldots )\) (A1) (C2)
\( - 2.96 < x < 1.34\;\;\;{\mathbf{OR}}\;\;\;\left] { - 2.96,{\text{ }}1.34} \right[\;\;\;{\mathbf{OR}}\;\;\;( - 2.96,{\text{ }}1.34)\) (A1)(ft)(A1) (C2)
Notes: Award (A1)(ft) for both correct endpoints of the interval, (A1) for correct strict inequalities (or correct open interval notation).
Follow through from part (b).
