2025 MI PU1 Promo Q3

2025 MI PU1 Promo Q3

Junior College 1
6 marks
  1. Sketch the graph of \(y=x+1-\frac{1}{x-5}\), indicating clearly the equations of the asymptotes and the coordinates of the axial intercepts.[3]
  2. By sketching a suitable graph on the same axes as your answer in part (i), solve the inequality \(x+1-\frac{1}{x-5}>\frac{1}{2}x+2\).[3]

Solution:

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Answer:Asymptotes \(x=5\), \(y=x+1\); \(1.44<x<5\) or \(x>5.56\)

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