Vertical Asypmptote or "Hole," part ISlide the value for "a." Recall that a rational function has roots where the numerator = 0, and vertical asymptotes where the denominator = 0, except when the two coincide -- then one of several things can happen. In this case, we're adjusting the roots ( +/- a). Note what happens when a = 1. Since this function is never defined at x = 1, we need an indirect method to talk about the obvious fact that, when a ≠ 1, we have a vertical asymptote at x = 1, while, when a = 1, we get a "hole" at (1, 2). The height of this hole is what we want to call the "limit as x approaches 1" of f(x) = (x² - 1) / (x - 1) Dave Matthews, Created with GeoGebra |