## Motivation

The expression $$y=x^2$$, which links the two pronumerals $$x$$ and $$y$$, can be thought of in several different ways.

In the early years of school, we seek pairs of values, such as $$(x,y) =(3,9)$$, which satisfy the equation. These ordered pairs determine a graph. In this case, the graph is the standard parabola. A formula is an equation relating different quantities using algebra. So $$y=x^2$$ is also a formula. In fact, $$y=x^2$$ is an example of a function, in the sense that each value of $$x$$ uniquely determines a value of $$y$$.

In this module, we will study the concept of a function. The formula $$A=\pi r^2$$ gives $$A$$ as a function of $$r$$. The formula $$V=\pi r^2h$$ expresses $$V$$ as a function of the two variables $$r$$ and $$h$$. In this module, we will only consider functions of one variable, such as the polynomial

$y = (x-1)(x-2)(x-3)(x-4).$

A clear understanding of the concept of a function and a familiarity with function notation are important for the study of calculus. The use of functions and function notation in calculus can be seen in the module Introduction to differential calculus.

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