By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, aiding OCR's MEI based arithmetic specification, has been up to date to check the necessities of the recent requisites, for first educating in 2004.
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Additional resources for A2 Pure Mathematics (C3 and C4)
The inverse function is given by f –1(x) = x, since the sign means ‘the positive square root of ’. 19 It is often helpful to restrict the domain of a function so that its inverse is also a function. e. sin –1 or arcsin) key on your calculator the answer is restricted to the range –90° to 90°, and is described as the principal value. 5 (…, –330°, –210°, 30°, 150°, …), only one of these, 30°, lies in the restricted range and this is the value your calculator will give you. 4 For each of the following functions, work out the inverse function, and draw the graphs of both the original and the inverse on the same axes, using the same scale on both axes.
0 0 Translate the triangle through and then stretch the image with a scale 3 factor of 2 parallel to the x axis. Stretch the triangle with a scale factor of 2 parallel to the x axis and then 0 . translate the image through 3 0 Translate the triangle through and then stretch the image with a scale 3 factor of 2 parallel to the y axis. Stretch the triangle with a scale factor of 2 parallel to the y axis and then 0 translate the image through . 3 () () () () () () () (v) (a) (b) Stretch the triangle with a scale factor of 2 parallel to the x axis and then stretch the image with a scale factor of 3 parallel to the y axis.
7). 7 (iii) The curve of y = cos (x – 60°) is obtained from that of y = cos x by a 60° translation of 0 . 8). 8 EXERCISE 3B 1 Starting with the graph of y = x 2, state the transformations which can be used to sketch each of the following curves. Specify the transformations in the order in which they are used and, where there is more than one stage in the sketching of the curve, state each stage. State the equation of the line of symmetry. (i) (iii) (v) (vii) 28 y = x2 – 2 y = (x – 2)2 y = (3x – 2)2 y = 2x 2 + 4x – 1 (ii) (iv) (vi) (viii) y = 3x 2 y = 3(x – 2)2 y = x 2 – 4x y = 3x 2 – 6x – 2 2 The diagram shows a sketch of the graph of y = f(x), where f(x) = x 2 + 4x.