The graph of $y = \frac{ax^2 + bx + c}{x + d}$ has a vertical asymptote with equation $x = -1$ a

Question

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 $b = 4$.[3] Hence find the range of values of $c$ if the graph has no stationary points.[2]

Accepted Answer

(a) $d=1,\ a=2,\ b=4$ (shown) (b) $c<2$

2025 ACJC P1 Q2

2025 ACJC P1 Q2

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