C3 June 2008 Q3

EdexcelOld spec12 marksFunctions (including |mod|)Sketching & Transforming Graphs

3.

Figure 1: graph of two line segments meeting at P, above and to the left of the origin; crosses the x-axis at -3 and at R, and the y-axis at Q
Figure 1

Figure 1 shows the graph of \(y = \mathrm{f}(x)\), \(x \in \mathbb{R}\).
The graph consists of two line segments that meet at the point \(P\).
The graph cuts the \(y\)-axis at the point \(Q\) and the \(x\)-axis at the points \((-3, 0)\) and \(R\).
Sketch, on separate diagrams, the graphs of

(a) \(y = |\mathrm{f}(x)|\), (2)
(b) \(y = \mathrm{f}(-x)\). (2)

Given that \(\mathrm{f}(x) = 2 - |x + 1|\),

(c) find the coordinates of the points \(P\), \(Q\) and \(R\), (3)
(d) solve \(\mathrm{f}(x) = \dfrac{1}{2}x\). (5)
‹ Previous50 of 115 in Functions (including |mod|)Next ›