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Chapter 1 | Functions and Graphs
Therefore, the zeros of f are x =0, 4, −1. iii. Combining the results from parts i. and ii., draw a rough sketch of f .
1.10 Consider the quadratic function f ( x ) =3 x 2 −6 x +2. Find the zeros of f . Does the parabola open upward or downward?
Mathematical Models A large variety of real-world situations can be described using mathematical models . A mathematical model is a method of simulating real-life situations with mathematical equations. Physicists, engineers, economists, and other researchers develop models by combining observation with quantitative data to develop equations, functions, graphs, and other mathematical tools to describe the behavior of various systems accurately. Models are useful because they help predict future outcomes. Examples of mathematical models include the study of population dynamics, investigations of weather patterns, and predictions of product sales. As an example, let’s consider a mathematical model that a company could use to describe its revenue for the sale of a particular item. The amount of revenue R a company receives for the sale of n items sold at a price of p dollars per item is described by the equation R = p · n . The company is interested in how the sales change as the price of the item changes. Suppose the data in Table 1.6 show the number of units a company sells as a function of the price per item.
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