Chapter 28: High School Review with Computing

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Chapter Summary
This chapter reviews the ideas of independent and dependent variables and parameters. We do this in the context of some down-to-earth applications. We want to help you to develop careful working habits to use in calculus. We need you to understand function notation in order to communicate ideas.

The idea of a function is useful on a very general level. We say that a quantity A (the answer) is a function of I (the input) over a certain domain of permissible values of I if each value of the input determines a unique answer. For example, the computer plot command Plot[ I ] is a function whose answer is a graph and whose input I is a certain string of other commands. Functional programming is an important part of modern computing, and many commands are given in function notation. In high school, you learned about real valued functions of a real input. These basic functions are important special cases of the next definition. Real valued functions of one variable are not always given by a formula. Non-formula functions arise in this course as solutions of differential equations such as the SIR equations in Chapter 2.

Definition: y Is a Real Valued Function of x, y=f[x] A real quantity y (the dependent variable) is a function of another real quantity x over a certain domain of values of x (the independent variable) if given an input value of x in the domain, there is a unique output value associated to it. We denote this input-output relationship by y=f[x].

Additional function notation is reviewed in Section CD-28.7 below.

We want to understand the abstract definition above in concrete terms and develop common terminology. This Chapter helps you answer the