the graph of f(x)=(6 - 4x)^2/(2x^2 - 5x + 12) has a horizontal asymptote at y =

Answer:

8

Explanation:

Step1: Identify the degrees of polynomials

The degree of the numerator $n=(6 - 4x)^2=36-48x + 16x^{2}$ is 2. The degree of the denominator $d = 2x^{2}-5x + 12$ is 2.

Step2: Use the horizontal - asymptote rule for equal - degree polynomials

When the degree of the numerator $n$ and the degree of the denominator $d$ are equal ($n = d$), the horizontal asymptote $y$ is given by the ratio of the leading coefficients. The leading coefficient of the numerator is 16 and the leading coefficient of the denominator is 2.

Step3: Calculate the ratio

$y=\frac{16}{2}=8$.