A power function is a mathematical expression of the form f(x) = k \cdot x^n , where k is a constant, x is the variable, and n is a real number. Power functions are used to model various phenomena in science and engineering, as they can describe relationships where one quantity varies as a power of another. Power functions can exhibit different behaviors depending on the value of n . For example, if n is positive, the function increases as x increases, while if n is negative, the function decreases. Common examples of power functions include the area of a square, which is proportional to the square of its side length, and the volume of a cube, which is proportional to the cube of its side length.