By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI dependent arithmetic specification, has been up to date to compare the necessities of the hot requisites, for first instructing in 2004.
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Extra resources for A2 Pure Mathematics (C3 and C4)
Mappings of these types are called functions. For example, x → x 2 and x → cos x° are both functions, because in each case for any value of x there is only one possible answer. 5. There are several different but equivalent ways of writing a function. For example, the function which maps x on to x 2 can be written in any of the following ways. ● y = x2 ● f(x) = x 2 ● f:x → x 2 Read this as ‘f maps x on to x 2’. It is often helpful to represent a function graphically, as in the following example, which also illustrates the importance of knowing the domain.
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.
The language of functions 3 Functions David Joanne Skiing Jonathan Returning home Louise To study abroad Paul Shamaila Business Karen This is an example of a mapping. The language of functions A mapping is any rule which associates two sets of items. In this example, each of the names on the left is an object, or input, and each of the reasons on the right is an image, or output. For a mapping to make sense or to have any practical application, the inputs and outputs must each form a natural collection or set.
A2 Pure Mathematics (C3 and C4) by Roger Porkess