<p>The graph of \(y = \frac{ax^2 + bx + c}{x + d}\) has a vertical asymptote with equation \(x = -1\) and an oblique asymptote with equation \(y = 2x + 2\). It is given that \(c \neq 2\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down the value of \(d\) and show that \(a = 2\) and \(b = 4\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the range of values of \(c\) if the graph has no stationary points.</span><span class="inline-marks">[2]</span></div></li></ol>

The graph of \(y = \frac{ax^2 + bx + c}{x + d}\) has a vertical asymptote with equation \(x = -1\) and an oblique asymptote with equation \(y = 2x + 2\). It is given that \(c \neq 2\).

Write down the value of \(d\) and show that \(a = 2\) and \(b = 4\).

Hence find the range of values of \(c\) if the graph has no stationary points.

Graphing Techniques

International Baccalaureate Higher Level Mathematics

2025 ACJC P1 Q2

2025 ACJC P1 Q2