Question

What is the horizontal asymptote of the function F(x)=(x-2)/(x-3)^2

O y = 0
O y = 1
O y = 2
oy=3

Answer 1

Y=0 there is no horizontal asymptote so it is 0

Answer 2

The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)²is;

A: y = 0

We are given the function;

f(x) = (x - 2)/(x - 3)²

Expanding the denominator gives us;

f(x) = (x - 2)/(x² - 6x + 9)

The rules for a horizontal asymptote are;

• If the degree of the polynomials in both denominator and numerator of a rational function are the same, then the horizontal asymptote will be expressed as the quotient of coefficients of the highest degree terms.

• If the polynomial of the denominator has a larger degree than the numerator, then the horizontal asymptote will be y = 0.

In our given expression, we can see that the degree of the denominator polynomial is greater than that of the numerator and as such the horizontal asymptote is y = 0.

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