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Modulus Function - Graphs of Modulus Function

Modulus Function - Graphs of Modulus Function

IP 3

The diagram above shows part of the graph of \(y=2-\left| 1-2x \right|.\)

  1. Write down the coordinates of \(A\) and \(B.\)

In each of the following cases, determine the number of intersections of the line \(y=mx+c\) with \(y=2-\left| 1-2x \right|\), justifying your answer.

  1. \(m=2\) and \(c<1\)
  2. \(m=-\frac{1}{2}\) and \(c<2\)

Source note: part (i) asks for B, but the diagram shows A at the vertex and C at the right x-intercept; B is not labelled. The solution gives the labelled points and the conditional interpretation if B was intended to mean C.

Solution:

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Answer:(i) \(A=(\frac12,2)\); B is unlabelled. The diagram’s \(C=(\frac32,0)\), also the answer if B was intended to mean C. (ii) One intersection. (iii) Two intersections.

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