Graphs of rational functions.

Delve into the fascinating world of rational functions, exploring their intricate behavior. When sketching their graphs, pay close attention to asymptotic behavior, which reveals how these functions approach infinity or certain values. Uncover the locations of stationary points, points where the function’s slope is zero, and axes intercepts, where the graph crosses the x and y-axes. Additionally, identify the elusive points of inflection, where the curvature of the graph changes. Proficiency in these aspects of rational functions empowers you to gain a deep understanding of their characteristics and applications in various mathematical contexts.