2021 VJC P1 Q2
2021 VJC P1 Q2
6 marks
Prelims
- Given that \(a\) is a positive constant, sketch the curve with equation \(y=\frac{x+a}{x-a}\). State the equations of any asymptotes and the coordinates of the points where the curve crosses the axes.[3]
- Solve the inequality \(\left| \frac{x+a}{x-a} \right|>1\).[2]
- Solve the inequality \(\frac{\left| x \right|+a}{\left| x \right|-a}>1\).[1]
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Answer:(i) Asymptotes: \(x=a\), \(y=1\); intercepts: \((-a,0)\), \((0,-1)\). (ii)(a) \(0<x<a\) or \(x>a\). (ii)(b) \(x<-a\) or \(x>a\).
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