<p>The function \(\mathrm{f}\) is defined by</p>
<p style="text-align: center">\[\mathrm{f}(x) = \begin{cases} x+4 & \text{for } -4 \le x &lt; -1, \\ x^2+2 & \text{for } -1 \le x &lt; 2. \end{cases}\]</p>
<p>It is given that&nbsp;\(\mathrm{f}(x) = \mathrm{f}(x+6)\) for all real values of \(x\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Sketch the graph of \(y = \mathrm{f}(x)\) for&nbsp;\(-6 \le x &lt; 6\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence sketch the graph of \(y = 2\mathrm{f}(x-1)\) for&nbsp;\(-6 \le x &lt; 6\).</span><span class="inline-marks">[3]</span></div></li></ol>

The function \(\mathrm{f}\) is defined by

\[\mathrm{f}(x) = \begin{cases} x+4 & \text{for } -4 \le x < -1, \\ x^2+2 & \text{for } -1 \le x < 2. \end{cases}\]

It is given that \(\mathrm{f}(x) = \mathrm{f}(x+6)\) for all real values of \(x\).

Sketch the graph of \(y = \mathrm{f}(x)\) for \(-6 \le x < 6\).

Hence sketch the graph of \(y = 2\mathrm{f}(x-1)\) for \(-6 \le x < 6\).

Functions

International Baccalaureate Higher Level Mathematics

2025 TMJC P2 Q3

2025 TMJC P2 Q3