C3 June 2006 Q3

EdexcelOld spec9 marksFunctions (including |mod|)Sketching & Transforming Graphs

3.

Figure 1: increasing curve y = f(x) through P(0, -2) on the y-axis and Q(3, 0) on the x-axis
Figure 1

Figure 1 shows part of the curve with equation \(y = \mathrm{f}(x)\), \(x \in \mathbb{R}\), where f is an increasing function of \(x\). The curve passes through the points \(P(0, -2)\) and \(Q(3, 0)\) as shown.

In separate diagrams, sketch the curve with equation

(a) \(y = |\mathrm{f}(x)|\), (3)
(b) \(y = \mathrm{f}^{-1}(x)\), (3)
(c) \(y = \tfrac{1}{2}\mathrm{f}(3x)\). (3)

Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.

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