Finding the Vertical Asymptotes of a Rational Function Find the values of a where the denominator is zero. If this value of a does not make the numerator zero, then the line x = a is a vertical asymptote. We will also look how the function behaves as x increases or decreases without bound. 2 days ago · b) Give the equation of the graph of any rational function that has a 'hole' where you would initially assume there was a vertical asymptote. c) Give the equation of the graph of any rational function that has no vertical asymptotes. d) Give the equation of the graph of any rational function that has no positive y-values defined in its range.

The vertical asymptotes correspond to x-values that make the denomiantor 0 (but those factors don’t cancel out on the numerator). { For f(x) = 2(x 1)(x+ 3) (x+ 4)(x 1), there is a vertical asymptote at x= 4 You can nd the horizontal asymptotes by comparing the degrees and leading terms on the numerator and denominator. To find the equations of the vertical asymptotes we have to solve the equation Near to the values x = 1 and x = -1 the graph goes almost vertically up or down and the function tends to either +∞ or -∞.

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