How can the area of a circle be written as a function of its radius?

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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. — function Plot of the cubic equation f(x) = x³ − 3x + 2. The plotted points are where changes in curvature occur.

In mathematics, the area of a circle can be expressed as a function of its radius by the formula:

$A (r) = π r^{2}$

In this function, $A$ represents the dependent variable (the area), and $r$ represents the independent variable (the radius). Because the area is determined by the square of the radius multiplied by the constant $π$ , this is classified as a polynomial function.12