Question

Find the horizontal asymptote of the function
A. none
B. x = 0
c.y=0
D.y = 1
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(x-1)(x-3)²(x+1)²
(x-2)(x+2)(x-1)(x+3)*

1. Horizontal asymptote y = 1.

### What is meant by horizontal asymptote?

• A slant asymptote has a specific instance known as a horizontal asymptote. A “recipe” for locating a rational function’s horizontal asymptote is as follows: Let deg D(x) and deg N(x) represent the degree of the denominator and the numerator, respectively. No horizontal asymptote exists.
• 1) If the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is y = 0. 2) The horizontal asymptote is y = c, where c is the ratio of the leading terms or their coefficients if the degree of the numerator and denominator are equal.
• The denominator of the function, n(x), can be used to find vertical asymptotes by solving the equation n(x) = 0 (note that this only works if the numerator, t(x), is not zero for the same x value). Find the function’s asymptotes. The graph exhibits a vertical asymptote at x = 1.
Find the horizontal asymptote of the function:
Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.
Horizontal asymptote y = 1.