<p>The diagram below shows the graph of \(y = \mathrm{f}(x)\).</p>
<div class="graph-block" data-graph-config="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" data-width="400" data-height="310" style="width:400px;height:310px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Sketch each of the following on a separate diagram, clearly indicating the \(y\)-intercept, turning point(s) and asymptote(s).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">\(y = 3\mathrm{f}(x + 2) - 1\)<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">\(y = -\mathrm{f}(x + 1) + 1\)<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">\(y = \mathrm{f}(-x - 1) + 2\)<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">\(y = \mathrm{f}(2x + 4) - 1\)<span class="inline-marks">[3]</span></div></li></ol>

The diagram below shows the graph of \(y = \mathrm{f}(x)\).

Sketch each of the following on a separate diagram, clearly indicating the \(y\)-intercept, turning point(s) and asymptote(s).

Composite Transformations

Transformations of Graphs

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Solution:

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