On many calculators, graphs of rational functions produce lines at vertical asymptotes. For example, graphing...

On many calculators, graphs of rational functions produce lines at vertical asymptotes. For example, graphing ${\displaystyle y=\frac{x-1}{x+1}}$ on the window [-4.9, 4.9] by [-4.9, 4.9] produces such a line at x=-1 on the TI-84 Plus and TI-89. But with the window [-4.7, 4.7] by [-4.7, 4.7] on a TI-84 Plus, or [-7.9, 7.9] by [-7.9, 7.9] on a TI-89, the spurious line does not appear. Experiment with this function on your calculator, trying different windows, and try to figure out an explanation for this phenomenon.