How Do You Explore Rational Functions For Algebra 2?
A rational function is any function that can be written as a ratio of two polynomials. Polynomial functions are sums of terms, like 4x^3+2x^2+1 or 5x^2+1. Before the advent of the graphing calculator, tables and graphs were calculated and drawn manually. The advent of scientific calculators like the TI-83 allow us to explore rational functions without having to plot tables and draw graphs by hand. Press the “Y=” button on your calculator to enter the Y Editor. Press the “1” button, followed by the “/” button, and the press the “X” button. This enters the function y=1/x into your calculator. Press the “Graph” key. Note the shape of the graph. Almost every rational function has a graph that is in two segments or more, without intercepts. In other words, it hugs the x and y axes, rather than crossing them. Find the vertical asymptote. This is the place where the graph increases or decreases without bounds, up or down the y-axis. Press the “Trace” key and trace the line upward along the y-
