# 3.1 Introduction to Functions

**Definition of Function • Independent and Dependent Variables • Functional Notation**

In many applications, it is important to determine how two different variables are related, where the value of one variable depends on the other. For example, the experiments performed by Galileo on free-falling objects led to the discovery of the formula $s\hspace{0.17em}=\hspace{0.17em}16{t}^{2}\hspace{0.17em},\hspace{0.17em}$ where `s` is the distance an object falls (in ft) and `t` is the time (in s). In this case, the distance depends on the time. Another example is that electrical measurements of voltage `V` and current `I` through a particular resistor would show that $V\hspace{0.17em}=\hspace{0.17em}kI\hspace{0.17em},\hspace{0.17em}$ where `k` is a constant. Here, the voltage depends on the current. In mathematics, whenever the value of one variable ...

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