Functions and their graphs
2.1 Introduction
The ability to produce a picture of a problem is an important step towards solving it. From the graph of a function, y = f (x), we are able to predict such things as the number of solutions to the equation f(x) = 0, regions over which it is increasing or decreasing, and the points where it is not defined.
Recognizing the shape of functions is an important and useful skill. Oscilloscopes give a graphical representation of voltage against time, from which we may be able to predict an expression for the voltage. The increasing use of signal processing means that many problems involve analysing how functions of time are effected by passing through some mechanical or electrical system.
In order to draw graphs ...
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