Chapter 1 | Functions and Graphs
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Figure 1.6 The graph of the data from Table 1.1 shows temperature as a function of time.
From the points plotted on the graph in Figure 1.6 , we can visualize the general shape of the graph. It is often useful to connect the dots in the graph, which represent the data from the table. In this example, although we cannot make any definitive conclusion regarding what the temperature was at any time for which the temperature was not recorded, given the number of data points collected and the pattern in these points, it is reasonable to suspect that the temperatures at other times followed a similar pattern, as we can see in Figure 1.7 .
Figure 1.7 Connecting the dots in Figure 1.6 shows the general pattern of the data.
Algebraic Formulas Sometimes we are not given the values of a function in table form, rather we are given the values in an explicit formula. Formulas arise in many applications. For example, the area of a circle of radius r is given by the formula A ( r ) = πr 2 . When an object is thrown upward from the ground with an initial velocity v 0 ft/s, its height above the ground from the time it is thrown until it hits the ground is given by the formula s ( t ) =−16 t 2 + v 0 t . When P dollars are invested in an account at an annual interest rate r compounded continuously, the amount of money after t years is given by the formula A ( t ) = Pe rt . Algebraic formulas are important tools to calculate function values. Often we also represent these functions visually in graph form.
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