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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
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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- Spring '12