Higher June 2022 Paper 2 Q21

EdexcelCurrent spec3 marksGraphical Transformations

21 The graph of \(y = \mathrm{f}(x)\) is shown on the grid below.

Grid showing the curve y = f(x): it comes down steeply from the top left, touches the x-axis at (-3, 0), rises to a maximum at (-1, 1), passes through the origin and goes down to (2, -4)
(a) On the grid above, sketch the graph of \(y = \mathrm{f}(-x)\) (1)

Here is a sketch of the graph of \(y = \tan x^\circ\)

Sketch of y = tan x degrees with vertical dashed asymptotes; the point Q is marked on the x-axis, the second zero to the right of O

The graph of \(y = \tan x^\circ\) is translated to give the graph of \(y = \mathrm{g}(x)\)

Following the translation the point \(Q\), shown on the graph above, moves to point \(R\).
Point \(R\) has coordinates \((90, -5)\)

(b) Find an expression for \(\mathrm{g}(x)\) in terms of \(x\). (2)
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