Function graphing is the visual representation of mathematical functions on a coordinate plane. It involves plotting points that represent pairs of input values (x) and their corresponding output values (y). Each point is marked based on its coordinates, allowing for a clear view of how the function behaves across different values. The resulting graph helps in understanding the relationship between variables and can reveal important features such as intercepts, slopes, and asymptotes. Common types of functions include linear, quadratic, and exponential, each with distinct shapes and characteristics that can be analyzed through their graphs.