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Values of a function and a composite read from its graph, and the sketch of a reflected and translated graph

Values of a function and a composite read from its graph, and the sketch of a reflected and translated graph

5 marks

The diagram shows the graph of \(y=f(x)\) for \(-2\leq x\leq8\). It consists of part of a parabola with vertex \((1,-4)\) and a straight-line segment joining \((3,0)\) to \((8,5)\).

  1. Use the graph to write down
    1. \(f(4)\)
    2. \((f\circ f)(4)\).[2]
  2. The function \(g\) is defined by \(g(x)=1-f(x)\) for \(-2\leq x\leq8\). Sketch the graph of \(y=g(x)\) on the same axes.[3]

Solution:

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Answer:(a)(i) \(1\) (a)(ii) \(-4\) (b) parabola from \((-2,-4)\) up to the maximum \((1,5)\) and down to \((3,1)\), then a straight line from \((3,1)\) to \((8,-4)\)

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