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vertical asymptote

[vertical asymptote|vertical asymptote] occurs at x = 2, corresponding to the (x + 3) factor in the denominator.

Definition

vertical asymptote occurs at x = 2, corresponding to the (x + 3) factor in the denominator. The graph heads towards positive infinity on both sides of the asymptote.

Mechanism

vertical asymptote At the vertical asymptote x = −3 corresponding to the ( x + 3 ) 2 factor of the denominator, the graph heads towards positive infinity on both sides of the asymptote, consistent with the behavior of the function f ( x ) = 1 x 2 .

Effects

Examine the behavior on both sides of each vertical asymptote to determine the factors and their powers. The degree of the numerator being larger than the degree of the denominator results in no horizontal asymptote.