This is because there are a couple of possible

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Unformatted text preview: o the x and y-axis but never crosses. Since there isn’t anything special about the axis themselves we’ll use the fact that the xaxis is really the line given by y = 0 and the y-axis is really the line given by x = 0 . In our graph as the value of x approaches x = 0 the graph starts gets very large on both sides of the line given by x = 0 . This line is called a vertical asymptote. Also, as x get very large, both positive and negative, the graph approaches the line given by y = 0 . This line is called a horizontal asymptote. Here are the general definitions of the two asymptotes. 1. The line x = a is a vertical asymptote if the graph increases or decreases without bound on one or both sides of the line as x moves in closer and closer to x = a . 2. The line y = b is a horizontal asymptote if the graph approaches y = b as x increases or decreases without bound. Note that it doesn’t have to approach y = b as x BOTH increases and decreases. It only needs to approach it on one side in order for it to be a horizontal asymptote. Determining asymptotes is actually a fairly simple process. First, let’s start with the rational function, f ( x) = ax n + L bx m + L where n is the largest exponent...
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