How do you find the vertical, horizontal or slant asymptotes for #(x^2 - 5x + 6)/( x - 3) #?

Answer 1

Elijah Allen

#y = 1#, at x = 3 and #y = x-2, x ne 3 to y = x-2#, for #x in R#.

No asymptotes.

As #y = ((x-2)(x-3))/(x-3)#, we can redefine y as follows.

#y = 1#, at x = 3 and

#y = x-2, x ne 3#

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Answer 2

Lily Anderson

To find the vertical asymptote, set the denominator equal to zero and solve for x. The equation x - 3 = 0 gives x = 3, so there is a vertical asymptote at x = 3.

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Since the degree of the numerator (2) is greater than the degree of the denominator (1), there is no horizontal asymptote.

To find the slant asymptote, perform polynomial long division or synthetic division to divide the numerator by the denominator. The result will be the equation of the slant asymptote.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.