By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI established arithmetic specification, has been up-to-date to check the necessities of the hot requisites, for first educating in 2004.
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Additional resources for A2 Pure Mathematics (C3 and C4)
Find the value of x for which y = 20 000. [MEI] Even, odd and periodic functions Several of the curves with which you are familiar have symmetry of one form or another. For example ● the curve of any quadratic in x has a line of symmetry parallel to the y axis ● the curve of y = cos x has the y axis as a line of symmetry ● the curves of y = sin x and y = tan x have rotational symmetry of order 2 about the origin ● all the trigonometrical graphs have a repeating pattern (translational symmetry).
You can decide whether an algebraic mapping is a function, and whether it has an inverse function, by looking at its graph. The curve or line representing a one-toone mapping does not double back on itself, has no turning points and covers the full domain and co-domain. 17 illustrates the functions f, g and h given on the previous page. 18). You can see that there are two distinct input values giving the same output: for example f(2) = f(–2) = 4. When you want to reverse the effect of the function, you have a mapping which for a single input of 4 gives two outputs, –2 and +2.
6. Using transformations to sketch the curves of functions Points on the x axis have a zero y co-ordinate, so are unchanged. 6 (ii) x The curve of y = cos – is obtained from that of y = cos x by a stretch of scale 2 factor 2 in the x direction. There will therefore be one complete oscillation of the curve in 720° (instead of 360°). x x 0 The curve of y = 3 + cos – is obtained from that of y = cos – by a translation . 7). 7 (iii) The curve of y = cos (x – 60°) is obtained from that of y = cos x by a 60° translation of 0 .
A2 Pure Mathematics (C3 and C4) by Roger Porkess