A function is a set of ordered pairs where each x-value is paired with exactly one y-value. The domain is the set of all possible x-values, and the range is the resulting y-values. The rate of change of a function can be found using the difference quotient or slope formula. A graph is a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point. Domain restrictions limit the possible input values of a function. Horizontal and vertical asymptotes provide information about the behavior of a rational function as x approaches positive or negative infinity.