1.13: A Rational Function and Its Asymptotes

4PM1/2R/June/2019 — Question 2 · 4 marks

1.13 diagram 1
Figure 1 shows part of the curve S\displaystyle S with equation
y=ax+bx+c,y=\frac{ax+b}{x+c},
where a\displaystyle a, b\displaystyle b and c\displaystyle c are integers.
The asymptote to S\displaystyle S parallel to the x\displaystyle x-axis is y=−2\displaystyle y=-2.
The asymptote to S\displaystyle S parallel to the y\displaystyle y-axis is x=−3\displaystyle x=-3.
The curve crosses the x\displaystyle x-axis at (4,0)\displaystyle (4,0).
The curve crosses the y\displaystyle y-axis at (0,p)\displaystyle (0,p), where p\displaystyle p is rational.
Find
(i) a\displaystyle a,
(ii) b\displaystyle b,
(iii) c\displaystyle c,
(iv) p\displaystyle p.
(4)