2022 EJC P1 Q1
2022 EJC P1 Q1
5 marks
Prelims
On the same axes, sketch the graphs of \(y=\left| x-a \right|\) and \(y=\left| x-b \right|\), where \(a\) and \(b\) are constants such that \(0 < a < b\).
You should show clearly the axial intercepts of both graphs. Hence solve the inequality \(\left| x-a \right|<\left| x-b \right|\).[5]
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Answer:Intercepts: \(y=|x-a|\) at \((a,0)\), \((0,a)\); \(y=|x-b|\) at \((b,0)\), \((0,b)\) \(\displaystyle x<\frac{a+b}{2}\)
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