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 can represent various types of relationships, such as linear, quadratic, or cubic, depending on the value of n . They are commonly used in algebra and calculus to model real-world phenomena. The graph of a power function varies based on the exponent n . For example, when n = 1 , the graph is a straight line, while n = 2 produces a parabola. Power functions are essential in fields like physics, engineering, and economics, as they help describe growth patterns and other relationships in data.