The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.
What is an asymptote?
An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.
What is the horizontal asymptote?
Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.
How to solve this problem?
Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.
The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.
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